This is a multi-part message in MIME format. ---------------0512111607496 Content-Type: text/plain; name="05-414.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="05-414.keywords" Kahler manifold, Einstein-Kahler metric, first Chern class, admissible functions, Tian's invariant, grassmannian ---------------0512111607496 Content-Type: application/postscript; name="Kahler_Invariant.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="Kahler_Invariant.ps" %!PS-Adobe-2.0 %%Creator: dvips 5.76 Copyright 1997 Radical Eye Software (www.radicaleye.com) %%Title: c:\mydocu~1\julien\articl~1\ju_art2g.dvi %%CreationDate: Sun Dec 11 19:18:13 2005 %%Pages: 13 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSCommandLine: dvips32.exe -a -d1 -F %+ c:\mydocu~1\julien\articl~1\ju_art2g.dvi -pj:C:\WINDOWS\TEMP\dv1.mfj %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.12.11:1918 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B /FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{ /nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{ /sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0] N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{ 128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N /rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup /base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx 0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff .1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N /cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add /gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{ dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1 adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2 idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg} {adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{ adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{] }if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{ cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin 0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict /eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X /IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for 65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0 0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V {}B /RV statusdict begin /product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{dup length product length le{dup length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false} ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false RMat{BDot} imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1 false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}B /d{ -3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{p 1 w} B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p a}B /bos{/SS save N}B /eos{SS restore}B end %%EndProcSet TeXDict begin 39158280 55380996 1000 600 600 (/MYDOCU~1/JULIEN/ARTICL~1/c:\mydocu~1\julien\articl~1\ju_art2g.dvi) @start %DVIPSBitmapFont: Fa msbm8 8 2 /Fa 2 81 df<91390FFC018091B5FC903903FC07E390390F7001FF90393CE0007FD9F1C0 13392601C380131DD80383C7120D4848140FD80E061407D80C0E1403EA1C0C00381501EA 301C13181270006092C7FC1338EAE03012C0AA12E0EA6038131812701230A2EA381CEA1C 0CD80C0E1570D80E0615F0D80707EC01E026038380EB03C0D801C114072600F1E0EB0F00 D93C70133E90390F3E01FC0103B512F0010014C0DA0FFEC7FC2C307EAE21>67 D80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fb xybtip10 10 2 /Fb 2 48 df<122012F07EA2127CA27EA27EA26C7EA212077FA26C7EA212017FA212007F A21378A2137CA2133C133EA2131EA3131FA27FA41480A21307A4EB0300112E8FAB00>15 D47 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fc xyatip10 10 2 /Fc 2 48 df<1302EB0780130FA2EB1F00A2133EA25BA25BA25B1201A2485AA25B1207A2 5B120FA290C7FCA25AA2121E123EA2123CA3127CA21278A412F8A25AA41260112E82AB00 >15 D<127012FCB4FCEA7FC0EA1FF0EA07FC3801FF8038007FF0EB1FFE903807FFC00100 13FC91381FFFE0020313FFDA007F13F8030713FCED003FEE01F82E11AC8E00>47 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fd cmex8 8 1 /Fd 1 102 df<017F14082601FFC0131C000701F01378489038FC01F0D83E00B512C000 78013F138000E090380FFE000040EB03F8260880AF27>101 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fe cmmi6 6 12 /Fe 12 120 df<127812FCA212FEA2127E1206A3120CA2121C121812301260124007107A 8513>59 D73 D77 D99 D<1338137CA2137813701300A7EA0780EA1FC0EA38 E01230EA60F0EAC1E0A3EA03C0A3EA0780A2EA0F0013041306EA1E0CA21318121CEA1E70 EA0FE0EA07800F237DA116>105 D<1418143C147CA214381400A7EB0780EB1FE01338EB 60F013C0A2EA0180A2380001E0A4EB03C0A4EB0780A4EB0F00A4131EA21238EA783CEAF8 381378EA70F0EA7FC0001FC7FC162D81A119>I<13F8EA0FF0A21200A2485AA4485AA438 07801E147FEB81C3EB8387380F060F495A1318EB700E4848C7FCA213FCEA1E7EEA3C0F80 EB0781158039780F0300A21402EB070600F0138CEB03F8386000F019247CA221>I<000F 13FC381FC3FF3931C707803861EC0301F813C0EAC1F0A213E03903C00780A3EC0F00EA07 80A2EC1E041506D80F00130C143C15181538001EEB1C70EC1FE0000CEB07801F177D9526 >110 D<3801E01F3903F07FC0390639C1E0390C3F80F0EB3E00001814F8013C137815F8 C65AA49038F001F0A3EC03E0D801E013C0EBF00715809038F80F003803DC3CEBCFF8EBC7 E001C0C7FC485AA448C8FCA2EA7FF012FF1D20809520>112 DI<380F01F0 381FC7F83831CE1CEA61F8EBF03C00C1137C13E014383803C000A4485AA448C7FCA4121E A2120C16177D951D>I119 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ff cmsy6 6 4 /Ff 4 55 df0 D20 D<903807FFF0133F5BD801FCC7FCEA03E0485A48C8FC121E121C123C5A1270A212F05AA2 B612F0A300E0C8FCA27E1270A212787E121C121E7E6C7EEA03E0EA01FC6CB512F0133F13 071C237A9D2A>50 D<1570A215F015E01401EC03C01580140715005C140E141E5C143814 78147014F05C1301495A5C130791C7FC5B130E131E131C133C5B137013F05B12015B1203 485A90C8FC5A120E121E121C123C5A127012F05A12601C2F77A300>54 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fg cmr6 6 8 /Fg 8 127 df<140C141E143FA24A7E146FECCFC014C790380187E090380383F0140349 6C7EEB0600497F157C49137E01387F133001706D7E136001E06D7E491307484880150348 C77F486E7E1206000E6E7E000C157C48157E163E48153F007FB71280A2B812C0A22A247C A332>1 D<130C1338137013E0EA01C0EA038013005A120EA25AA25AA312781270A312F0 AB1270A312781238A37EA27EA27E7E1380EA01C0EA00E013701338130C0E317AA418>40 D<12C012707E7E7E7E7E1380EA01C0A2EA00E0A21370A313781338A3133CAB1338A31378 1370A313E0A2EA01C0A2EA038013005A120E5A5A5A12C00E317CA418>I<1438B2B712FE A3C70038C7FCB227277C9F2F>43 D<13E01201120712FF12F91201B3A7487EB512C0A212 217AA01E>49 DI61 D<000F1380381F81C0383FF780387BFF00EAE07EEA403C12067AA11E> 126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fh callig15 15 1 /Fh 1 72 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fi cmcsc10 12 42 /Fi 42 123 df<121FEA3F80EA7FC0EAFFE0A313F0A2127FEA3FB0EA1F301200A4137013 60A213E013C0A2120113801203EA07001206120E5A5A12300C1E768A20>44 D<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B768A20>46 D<1438147814F81303130F13FFB5FC13F713071200B3B3B0497E497EB712C0A3224276C1 37>49 D<49B4FC010F13F0013F13FC9038FC03FF2601E00013C0D807C0EB3FE048486D7E 90C76C7E001E6E7E4881003814030078811270007C80B416807F7F81A46C485B6CC7FCC8 FC17005DA25E15075E4B5AA24B5A5E4B5A4B5A4BC7FC5D4A5A4A5A4A5AEC0FC04A5A92C8 FC143E5C5C495A4948EB0380EB078049C7FC011EEC07005B5B5B48485C485A49141E48B6 12FE5A5A5A5AB75AA329427AC137>II<16E015011503A21507150FA2151F153FA2157F15 EF15CF1401EC038F150F1407140E141CA214381470A214E0EB01C0A2EB0380EB0700A213 0E5B131813385B136013E0485A485AA248C7FC120EA25A5AA25A5AB812F8A3C8381FE000 AC4B7E4B7E027FB512F8A32D437CC237>I<0007151801E014F801FEEB1FF090B65A5E5E 93C7FC15FC15F015C0D90FFEC8FC90CAFCADEC7FC0903803FFF890380F807E90381C003F 01786D7E01E0EB0FE0496D7E5B6F7E90C77FC8120182A28281A21780A5123EEA7F8012FF 7FA34915005D48C7FC00705DA200784A5A1238003C4A5A6C5D6C4A5A6D495A6C6C495AD8 03F049C7FC3900FE03FE90387FFFF8011F13C0D903FEC8FC29447AC137>II<1638167CA316FEA34B7EA24B7FA34B7F167FA2030E7F163FA24B6C7EA2033C7FED 380FA203787FED7007A203E07F1603A24A486C7EA20203814B7EA202078192C7127FA202 0E81173FA24A6E7EA2023C810238140FA2027FB67EA302E0C7EA07FE17030101824A80A2 0103834A80A249C97F187FA2010E707EA2011E83181F133E85137E48B483000701C0ED7F FFB500FC021FB512FEA347477CC651>65 DII70 D<922603FF801306033F01F0130E4AB500FE131E02079038003F80DA1FF0903807C03EDA 7FC0903801F07E4948C812F8D903FCED3CFE4948151F4948150F4948150749481503495A 49C91201481700485A49177E12074848173EA2001F181E5BA2123F49170E127FA396C7FC 5B12FFAC007F047FB512FC7FA2DD001F1300F007FE003F17037F121FA27F120FA26C7E12 037F6C7E7E6D7E6D7E6D6C15076D7E6D6C150FD903FE151E6D6CED3C7E9026007FC0ECF8 3EDA1FF8903803F01EDA07FF90381FC00E020190B5EA0006DA003F01FC90C7FC030313C0 464879C555>I75 DIII80 D82 D<49B46C13C0010FEBF001013FEBFC039038FF007FD801F8EB0F87 4848EB03E7D807C0EB01FF48487F001F157F90C8123F003E151FA2007E150F127C160712 FC1603A37E16017EA27F6C6C91C7FC7F7FEA3FFCEBFFC06C13FC6CEBFFC015FC6CECFF80 6C15E0C615F86D80011F80010380D9003F1480020314C0EC003F030313E01500EE7FF016 1FA2EE0FF8160712E01603A21601A37EA217F07E16037E17E06C15076C16C06DEC0F806D 141F6DEC3F00D8F8F8147E017F5C3AF01FE007F00107B55AD8E00191C7FC39C0001FFC2D 4879C53D>I<003FBAFCA3903BF8000FFE000701C06D48130090C7163F007EF01F80007C 180FA200781807A300701803A548F001C0A5C893C7FCB3B3A44B7E92383FFF8049B712F0 A342437BC24E>I89 D<157015F8A34A7EA24A 7EA34A7E81A291380E3F80A2021E7FEC1C1FA24A6C7EA34A6C7EA202F07FECE003A24948 6C7EA349486C7EA201078091C77EA249B67EA24981011CC7121FA2013C810138140FA249 6E7EA201F081491403120183486C140100074B7ED81FF84A7EB5027F13F8A335357CB43D >97 DI<4AB4EB0180021FEBF00391 B5EAFC0701039038007E0FD907F8EB0F9FD91FE0EB03DF4948EB01FF01FFC8FC4848157F 4848153FA24848151F4848150F121F491507123F5BA2007F1603A3484892C7FCAB6C7EEF 0380A2123FA27F001F16076D1600000F5E6C6C150E6C6C151E171C6C6C153C6C6C5DD93F C05C6D6CEB03E0D907F8495A902703FF807FC7FC0100EBFFFC021F13F00201138031357B B33B>III104 DI107 DIII II114 D<90390FF0018090387FFE 0348B512873907F00FEF390FC001FF48C7FC003E143F151F5A150F5A1507A36C1403A27E 6C91C7FC6C7E7FEA3FF8EBFF806C13FC6CEBFFC06C14F06C80C614FE011F7F01031480D9 001F13C014019138003FE0151F150FED07F0150312E01501A37EA216E06C1403A26CEC07 C06CEC0F806C6CEB1F0001E0133ED8FBFE13FC00F0B55AD8E01F13E0D8C00390C7FC2435 7BB32E>I<007FB812C0A3903A8007FC003F277E0003F8130F007C160700781603007016 01A200F017E0A2481600A6C71600B3AA4A7E4A7E010FB512FEA333327CB13B>II119 D121 D<003FB7FCA39039FC0001FE01E0130301 8014FC90C7EA07F8003E140F003C15F0007CEC1FE00078EC3FC0A2ED7F800070ECFF00A2 4A5A4A5AC712075D4A5A141F5D4A5A4A5AA24AC7FC495AA2495A495A130F4A1307495A13 3F5C495A49C7FC160F485A485AA24848141E485A001F153E49147E484814FE007F140349 131FB7FCA328337BB232>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fj cmr9 9 19 /Fj 19 89 df<123C127EB4FCA21380A2127F123D1201A412031300A25A1206120E120C 121C5A5A126009177AB315>39 D<15E0A34A7EA24A7EA34A7EA3EC0DFE140CA2EC187FA3 4A6C7EA202707FEC601FA202E07FECC00FA2D901807F1507A249486C7EA301066D7EA201 0E80010FB5FCA249800118C77EA24981163FA2496E7EA3496E7EA20001821607487ED81F F04A7ED8FFFE49B512E0A333367DB53A>65 D68 DIIIII<017FB5FCA39038003FE0EC1FC0B3B1127E B4FCA4EC3F805A0060140000705B6C13FE6C485A380F03F03803FFC0C690C7FC20357DB2 27>I76 DII I82 D<90381FE00390387FFC0748B5FC3907F01FCF390F 8003FF48C7FC003E80814880A200788000F880A46C80A27E92C7FC127F13C0EA3FF013FF 6C13F06C13FF6C14C06C14F0C680013F7F01037F9038003FFF140302001380157F153FED 1FC0150F12C0A21507A37EA26CEC0F80A26C15006C5C6C143E6C147E01C05B39F1FC03F8 00E0B512E0011F138026C003FEC7FC22377CB42B>I<007FB712FEA390398007F001D87C 00EC003E0078161E0070160EA20060160600E01607A3481603A6C71500B3AB4A7E011FB5 12FCA330337DB237>III<267FFFFC90B512C0A3000101E090381FF80026007F80EB0FC001 3F6E5A6E91C7FC6D6C130E010F140C6E5B6D6C133801035C6E13606D6C13E06D6C485A5E DA7F83C8FCEC3FC715C6EC1FECEC0FFC5D14076E7EA26E7E815C6F7E9138063FC0140E4A 6C7E9138180FF0EC380702707F91386003FCECC0010101804A6C7E49C77E4981010E6E7E 010C6E7E131C496E7E01786E7E13FCD807FEEC1FFEB56C90B512F8A335337EB23A>88 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fk cmbx9 9 10 /Fk 10 58 df48 D<147814F81303131FEA03FFB5FCA3EAFC1F1200B3B2007FB5 12FEA41F317AB02C>III<151F5D5DA25D 5C5C5C5CA25C143D147D14F9EB01F114E1EB03C1EB0781130FEB1F01133E133C137813F0 1201EA03E0EA07C01380EA0F00121E123E5A5AB712FEA4C700031300A80103B512FEA427 317EB02C>I<000C140ED80FE013FE90B5FC5D5D5D5D5D92C7FC14FC14F091C8FC1380A6 EB87FE9038BFFFC090B512F09038FC0FF89038E003FE01C07F497E01001480000E6D13C0 C8FCA216E0A3121FEA7F807F487EA316C05B5CD87F801480D87C0014006C5B393F8007FE 391FE01FFC0007B512F06C14C0C691C7FCEB1FF823327CB02C>II<123C123F90B612F8A44815F0 16E016C0168016005D007CC7127E00785C4A5A00F8495A48495A4A5A4A5AC7FC4AC7FC14 7E14FE5C13015C1303A2495AA2130FA2131FA25C133FA4137FA96D5AA2010FC8FC25337B B12C>III E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fl cmtt10 10 14 /Fl 14 121 df<121FEA3F80EA7FC0EAFFE0A5EA7FC0EA3F80EA1F000B0B708A2C>46 D64 D<3801FFF0000713FE001F6D7E15E048809038C01FF81407EC 01FC381F80000006C77EC8127EA3ECFFFE131F90B5FC1203120F48EB807E383FF800EA7F C090C7FC12FE5AA47E007F14FEEB8003383FE01F6CB612FC6C15FE6C14BF0001EBFE1F3A 003FF007FC27247CA32C>97 D101 DII<1307EB1FC0 A2497EA36D5AA20107C7FC90C8FCA7387FFFC080B5FC7EA2EA0007B3A8007FB512FCB612 FEA36C14FC1F3479B32C>105 D<140EEC3F80A2EC7FC0A3EC3F80A2EC0E0091C7FCA748 B512804814C0A37EC7120FB3B3A2141F003C1480007E133FB414005CEB01FEEBFFFC6C5B 5C001F5B000790C7FC1A467CB32C>I<387FFFE0B57EA37EEA0003B3B3A5007FB61280B7 12C0A36C158022337BB22C>108 D<397FF01FE039FFF87FFC9038F9FFFE01FB7F6CB6FC 00019038F03F80ECC01F02807FEC000F5B5BA25BB3267FFFE0B5FCB500F11480A36C01E0 140029247FA32C>110 D114 D<3A7FF003FF80486C487FA3007F7F0001EB000FB3A3151FA2153F6D137F 3900FE03FF90B7FC6D15807F6D13CF902603FE07130029247FA32C>117 D<3A7FFF01FFFCB514FE148314016C15FC3A03E0000F80A26D131F00011500A26D5B0000 143EA26D137E017C137CA2017E13FC013E5BA2EB3F01011F5BA21483010F5BA214C70107 5BA214EF01035BA214FF6D90C7FCA26D5A147C27247EA32C>I<3A3FFF03FFF048018713 F8A36C010313F03A00FC007E005D90387E01F8013F5BEB1F83EC87E090380FCFC0903807 EF80EB03FF6D90C7FC5C6D5A147C14FE130180903803EF80903807CFC0EB0FC7EC83E090 381F01F0013F7FEB7E00017C137C49137E0001803A7FFF01FFFC1483B514FE6C15FC1401 27247EA32C>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fm cmsy10 10 1 /Fm 1 16 df15 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fn cmti10 10 18 /Fn 18 117 df<387FFFF8A2B5FCA214F0150579941E>45 D48 D<15181538157815F01401140314 07EC0FE0141F147FEB03FF90383FEFC0148FEB1C1F13001580A2143FA21500A25CA2147E A214FEA25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7 FC497EB61280A31D3877B72A>II<010314186E13F8903907F007F091B512E016C01600495B15F8010E13E002 0CC7FC011EC8FC131CA3133C1338A313781370A2147F9038F3FFC09038EF83E09038FC01 F0496C7E485A497F49137CC8FC157EA315FEA41401000C5C123F5A1403485C5A4A5A12F8 00E05C140F4A5A5D6C49C7FC0070137E00785B387C01F8383E07F0381FFFC06C90C8FCEA 01F8253A77B72A>53 D<133C137E13FF5AA313FE13FCEA00701300B2120EEA3F80127F12 FFA31300127E123C102477A319>58 D<0103B612FEEFFFC018F0903B0007F8000FF84BEB 03FCEF00FE020F157FF03F804B141F19C0021F150F19E05D1807143F19F05DA2147FA292 C8FCA25C180F5CA2130119E04A151FA2130319C04A153FA201071780187F4A1600A2010F 16FEA24A4A5A60011F15034D5A4A5D4D5A013F4B5A173F4A4AC7FC17FC017FEC03F84C5A 91C7EA1FC04949B45A007F90B548C8FCB712F016803C397CB83F>68 D<0107B8FCA3903A000FF000034BEB007F183E141F181E5DA2143FA25D181C147FA29238 000380A24A130718004A91C7FC5E13015E4A133E167E49B512FEA25EECF8000107147C16 3C4A1338A2010F147818E04A13701701011F16C016004A14031880013F150718004A5CA2 017F151E173E91C8123C177C4915FC4C5A4914070001ED7FF0B8FCA25F38397BB838>I< 14F8EB07FE90381F871C90383E03FE137CEBF801120148486C5A485A120FEBC001001F5C A2EA3F801403007F5C1300A21407485C5AA2140F5D48ECC1C0A2141F15831680143F1587 007C017F1300ECFF076C485B9038038F8E391F0F079E3907FE03FC3901F000F0222677A4 2A>97 D<133FEA1FFFA3C67E137EA313FE5BA312015BA312035BA31207EBE0F8EBE7FE90 38EF0F80390FFC07C013F89038F003E013E0D81FC013F0A21380A2123F1300A214075A12 7EA2140F12FE4814E0A2141F15C05AEC3F80A215005C147E5C387801F8007C5B383C03E0 383E07C0381E1F80D80FFEC7FCEA01F01C3B77B926>I<147F903803FFC090380FC1E090 381F0070017E13784913383901F801F83803F003120713E0120FD81FC013F091C7FC485A A2127F90C8FCA35A5AA45AA3153015381578007C14F0007EEB01E0003EEB03C0EC0F806C EB3E00380F81F83803FFE0C690C7FC1D2677A426>I<147F903803FFC090380FC1E09038 3F00F0017E13785B485A485A485A120F4913F8001F14F0383F8001EC07E0EC1F80397F81 FF00EBFFF891C7FC90C8FC5A5AA55AA21530007C14381578007E14F0003EEB01E0EC03C0 6CEB0F806CEB3E00380781F83803FFE0C690C7FC1D2677A426>101 D104 DI108 DI<39 03C003F0390FF01FFC391E783C0F381C7C703A3C3EE03F8038383FC0EB7F800078150000 701300151CD8F07E90C7FCEAE0FE5BA2120012015BA312035BA312075BA3120F5BA3121F 5BA3123F90C9FC120E212679A423>114 D116 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fo cmsy8 8 14 /Fo 14 107 df0 D<006015C000E014016C14030078EC07806C EC0F006C141E6C5C6C6C5B6C6C5B6C6C485A6C6C485A90387807806D48C7FCEB1E1E6D5A EB07F86D5A6D5A497E497EEB0F3CEB1E1E497E496C7E496C7E48486C7E48486C7E484813 7848C77E001E80488048EC078048EC03C048140100601400222376A137>2 D<130C131EA50060EB01800078130739FC0C0FC0007FEB3F80393F8C7F003807CCF83801 FFE038007F80011EC7FCEB7F803801FFE03807CCF8383F8C7F397F0C3F8000FCEB0FC039 781E078000601301000090C7FCA5130C1A1D7C9E23>I 14 D20 D<12E012F812FEEA3F80EA0FE0EA03F8EA00FEEB3F80EB0FE0EB03F8EB00FC14 3FEC0FC0EC07F0EC01FCEC007FED1FC0ED07F0ED01FCED007FEE1FC01607161FEE7F00ED 01FCED07F0ED1FC0037FC7FCEC01FCEC07F0EC0FC0023FC8FC14FCEB03F8EB0FE0EB3F80 01FEC9FCEA03F8EA0FE0EA3F80007ECAFC12F812E0CBFCAD007FB71280B812C0A22A3B7A AB37>I<137813FE1201A3120313FCA3EA07F8A313F0A2EA0FE0A313C0121F1380A3EA3F 00A3123E127E127CA35AA35A0F227EA413>48 DI<91B512 C01307131FD97F80C7FC01FCC8FCEA01F0EA03C0485A48C9FC120E121E5A123812781270 A212F05AA3B712C0A300E0C9FCA37E1270A212781238123C7E120E120F6C7E6C7EEA01F0 EA00FCEB7F80011FB512C013071300222B7AA52F>I<023FB512F80107B6FC011F15E001 7F15C09026F8001EC7FCD803C05B4848137C000F147890C712F8121E0018495AC7FCA24A 5AA34A5AA3140F5DA3141F92C8FCA35C143EA35CA2147814F85C010114064A131C010314 3C4A5B49485B000FB612C0003F5D484AC7FCB612F02D2D81AC27>73 D92 D<141F14FFEB03F0EB0FC0EB1F8014005B133EB3A2137E137C13FC485A485AEA7FC048C7 FCEA7FC0EA03F06C7E6C7E137C137E133EB3A2133F7F1480EB0FC0EB03F0EB00FF141F18 437BB123>102 D<12FCB47EEA0FE0EA01F0EA00FC137C137E133EB3A37F1480130FEB07 E0EB01FEEB007FEB01FEEB07E0EB0F80131F1400133EB3A3137E137C13FCEA01F0EA0FE0 EAFF8000FCC7FC18437BB123>I<12E0B3B3B3AD034378B114>106 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fp cmex10 12 28 /Fp 28 112 df0 D<12E07E12787E7E7E7F6C7E6C7E7F12016C7E7F137C137E7FA26D7EA26D7EA26D7EA36D 7EA2801301A2801300A280A2147EA2147FA4801580A7EC1FC0B3A5EC3F80A715005CA414 7EA214FEA25CA213015CA213035CA2495AA3495AA2495AA249C7FCA2137E137C13FC5B48 5A12035B485A485A90C8FC121E5A5A5A5A1A777C832E>II I8 D<12F012FEEAFFC0EA3FF0EA07FCEA01FE6C6C7EEB3FC06D7E130F801307801303B3B080 1301A26D7E806E7E6E7E6E7EEC07F8EC01FC9138007F80ED1FE01503151FED7F80913801 FC00EC07F8EC1FE04A5A4A5A4AC7FC5C495AA213035CB3B013075C130F5C131F495AEBFF 804848C8FCEA07FCEA3FF0EAFFC048C9FC12F0237775833A>I<12F0B3B3B3AA04407281 21>12 D<00F0EB03C0B3B3B3AA1A40728137>I<16F01501ED03E0ED07C0ED0F80ED1F00 5D157E5D5D14014A5A4A5A4A5AA24A5A143F92C7FC147EA25C13015C13035C13075C130F 5C131FA2495AA349C8FCA213FEA312015BA212035BA21207A25BA2120FA25BA2121FA45B A2123FA55B127FA990C9FC5AB3AA7E7FA9123F7FA5121FA27FA4120FA27FA21207A27FA2 1203A27F1201A27F1200A3137FA26D7EA36D7EA2130F801307801303801301801300147E A28081141F6E7EA26E7E6E7E6E7E140081157E8181ED0F80ED07C0ED03E0ED01F0150024 B26E833B>16 D<12F07E127C7E7E6C7E7F6C7E6C7E12017F6C7E137E7FA26D7E80130F6D 7EA26D7E80130180130080147E147F8081A26E7EA36E7EA26E7EA3811403A2811401A281 A21400A281A281A21680A4153FA216C0A5151F16E0A9150F16F0B3AA16E0151FA916C015 3FA51680A2157FA41600A25DA25DA21401A25DA214035DA214075DA34A5AA24A5AA34A5A A292C7FC5C147E14FE5C13015C13035C495AA2495A131F5C49C8FCA2137E5B485A5B1203 485A485A5B48C9FC123E5A5A5A24B27C833B>I<171E173E177C17F8EE01F0EE03E0EE07 C0160FEE1F80EE3F00167E167C16FC4B5A4B5A15075E4B5A4B5A153F93C7FC5D15FE5D14 015D14034A5AA24A5AA24A5AA24A5AA24AC8FCA214FEA213015C13035C1307A25C130F5C 131FA25C133FA3495AA349C9FCA35A5BA312035BA31207A25BA2120FA35BA3121FA35BA3 123FA55BA2127FAB485AB3B06C7EAB123FA27FA5121FA37FA3120FA37FA31207A27FA212 03A37F1201A37F7EA36D7EA36D7EA3131F80A2130F80130780A21303801301801300A214 7FA26E7EA26E7EA26E7EA26E7EA26E7E140181140081157F8182151F6F7E6F7E8215036F 7E6F7E167C167E82EE1F80EE0FC01607EE03E0EE01F0EE00F8177C173E171E2FEE6B8349 >I<12F07E127C7E7E6C7E6C7E7F6C7E6C7E6C7E137C137E7F6D7E80130F6D7E6D7E8013 01806D7E147E147F80816E7EA26E7EA26E7EA26E7EA26E7EA26E7EA2818182153F82A215 1F82150F82A2150782A36F7EA36F7EA38281A31780167FA317C0A2163FA217E0A3161FA3 17F0A3160FA317F8A51607A217FCABEE03FEB3B0EE07FCAB17F8A2160FA517F0A3161FA3 17E0A3163FA317C0A2167FA21780A316FF1700A35D5EA34B5AA34B5AA35E150FA25E151F 5E153FA25E157F93C7FC5D5DA24A5AA24A5AA24A5AA24A5AA24A5AA24A5A92C8FC5C147E 14FE495A5C13035C495A495A131F5C49C9FC137E137C13FC485A485A485A5B485A48CAFC 123E5A5A5A2FEE7C8349>I[51 298 104 131 79 32 D[<12F87E127E7E7F121F6C 7E6C7E7F6C7E12016C7E7F137F7F806D7E6D7EA26D7E8013036D7EA26D7E808081143F81 141F816E7EA26E7EA26E7EA26E7EA36E7EA26F7EA282153FA282151F82150FA2821507A2 82150382A3150182A28183A3707EA4707EA483161FA483160FA383A31607A383A31603A3 83A582A21880A882A218C0AD177F18E0B3B3A618C017FFAD1880A25EA81800A25EA55FA3 1607A35FA3160FA35FA3161F5FA4163F5FA44C5AA44C5AA394C7FC5DA25E1503A35E1507 5EA2150F5EA2151F5E153F5EA2157F5EA24BC8FCA24A5AA34A5AA24A5AA24A5AA24A5A5D 143F5D147F92C9FC5C5C495AA2495A13075C495AA2495A495A91CAFC5B13FE5B485A1203 485A5B485A485A123F90CBFC127E5A5A>51 298 125 131 79 I56 D58 D<913807FF80B3B3B04A1300A55D141FA35D143F5DA2147F5D14FF5DA2495B5D5B4990C7 FC5C130F5C495A495A495AA2495A485B4890C8FCEA07FC485A485AEA7FE0EAFF8090C9FC 12FCB4FC7FEA7FE0EA1FF06C7E6C7E6CB4FC6C7F6C7F6D7EA26D7E6D7E6D7E801307806D 7F7F816D7FA281147F81143FA281141F81A3140F81A56E1380B3B3B021B56F8059>60 D62 D80 D<007C193EA200FE197FB3 B3B3AE6C19FFA26C19FEA26D1701A26C6CEF03FCA2001F19F86D17076D170F000F19F06C 6CEF1FE06D173F6C6CEF7FC06C6CEFFF806E5D6C01E0030713006D6C4B5AD93FFCED3FFC 6DB4EDFFF86D01E001075B6D01FE017F5B010190B712806D94C7FC023F15FC020F15F002 011580DA003F01FCC8FC030313C048647B7F53>83 D88 DI<1B3FF3FFC0973803E0F0973807C03897380F80 1C081F137E97383F01FEF303FF1A7E1AFE1AFC1901A2963903F801FEF300781C004F5AA2 190FA262191FA34F5AA44F5AA319FF97C8FCA360A261A21803A3611807A461180FA44E5A A4183FA261A2187FA361A218FFA44D5BA55F96C9FCA35FA360A2170FA460171FA460173F A54D5AA54D5AA45E60A55E60A44C90CAFCA54C5AA55F161FA45F163FA45FA2167FA35FA3 16FF5FA54B5BA494CBFCA25DA35EA21507A25EA44B5AA45E151FA45E153FA35EA2157FA2 5EA315FF93CCFCA34A5AA44A5AA35D14075DA2140F5D121E397F801FC0EAFFC05D143F92 CDFC5C147E6C485AEA7E00383801F86C485A380F07C03803FF80D800FCCEFC58DD7B7F37 >I101 D 104 DI110 D<12F012FE6C7E13E0EA3FF8EA0FFCEA03FFC67F6D7E6D7E6D7E6D7E6D7E6D7EA26D7E7F A281147FB3B3AF81143FA281141F81140F8114076E7E6E7E6E7E6F7E6F7EED1FF0ED07F8 ED01FE923800FF80163FA216FF923801FE00ED07F8ED1FF0ED3FC04B5A4BC7FC4A5A4A5A 4A5A140F5D141F5D143F5DA2147F5DB3B3AF14FF92C8FCA25B495AA2495A495A495A495A 495A495A000390C9FCEA0FFCEA3FF8EAFFE0138048CAFC12F029B2748342>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fq msbm10 12 4 /Fq 4 83 df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ndDVIPSBitmapFont %DVIPSBitmapFont: Fr cmr8 8 11 /Fr 11 127 df<156015F0A24A7E4A7EA24A7E1406EC0E7F140C91381C3F8014184A6C7E 150F02607F150702C07F1503D901807F1501D903007F496D7E1306010E147F130C011C6E 7E131801386E7E1330496E7E160749811603484881160148C87F486F7E1206000E167F12 0C001CEE3F801218003FB812C0A24817E0A2B912F0342F7DAE3B>1 D<013FB5FCA29038007F806EC8FCA6903801FFE0011F13FE90397F3F3F80D801F8EB07E0 D807E0EB01F8D80FC06D7ED81F80147ED83F0080481680A2007E151F00FE16C0A5007E16 80007F153FA26C1600D81F80147ED80FC05CD807E0495AD801F8EB07E0D8007FEB3F8090 261FFFFEC7FC010113E0D9003FC8FCA64A7E013FB5FCA22A2D7CAC33>8 D<010FB512C0A29026001FE0C7FC6E5AA500FEED01FCD8FF801407001F16E001C0140F00 0F16C001E0141F00071680A9D803F0EC3F00A4D801F8147EA2D800FC5C017EEBC1F8013F EBC3F090391F8FC7E0903907EFDF80902601FFFEC7FC9038003FF0EC0FC0A64A7E010FB5 12C0A22E2D7CAC37>I<13031307130E131C1338137013F0EA01E013C01203EA0780A2EA 0F00A2121EA35AA45AA512F8A25AAB7EA21278A57EA47EA37EA2EA0780A2EA03C0120113 E0EA00F013701338131C130E1307130310437AB11B>40 D<12C07E12707E7E7E120FEA07 80120313C0EA01E0A2EA00F0A21378A3133CA4131EA5131FA2130FAB131FA2131EA5133C A41378A313F0A2EA01E0A2EA03C013801207EA0F00120E5A5A5A5A5A10437CB11B>I43 D48 D<130C133C137CEA03FC12FFEAFC7C1200B3B113FE387FFFFEA2172C7AAB23>II61 D<38078008380FE01C381FF838383FFF F038707FE038E01FC03840078016077AAC23>126 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fs cmsy10 12 23 /Fs 23 111 df<007FB912E0BA12F0A26C18E03C04789A4D>0 D<121FEA3F80EA7FC0EA FFE0A5EA7FC0EA3F80EA1F000B0B789E1C>I<0060160600F8160F6C161F007E163F6C16 7E6C6C15FC6C6CEC01F86C6CEC03F06C6CEC07E06C6CEC0FC06C6CEC1F80017EEC3F006D 147E6D6C5B6D6C485A6D6C485A6D6C485A6D6C485A6D6C485ADA7E3FC7FCEC3F7E6E5A6E 5A6E5AA24A7E4A7EEC3F7EEC7E3F4A6C7E49486C7E49486C7E49486C7E49486C7E49486C 7E49C7127E017E8049EC1F804848EC0FC04848EC07E04848EC03F04848EC01F84848EC00 FC48C9127E007E163F48161F48160F00601606303072B04D>I8 D<49B4FC010F13E0013F13F8497F3901FF01FF3A03F8003F 80D807E0EB0FC04848EB07E04848EB03F090C71201003EEC00F8007E15FC007C157C0078 153C00F8153EA248151EA66C153EA20078153C007C157C007E15FC003E15F86CEC01F06D 13036C6CEB07E06C6CEB0FC0D803F8EB3F803A01FF01FF0039007FFFFC6D5B010F13E001 0190C7FC27267BAB32>14 D<007FBA1280BB12C0A26C1980CEFCB0007FBA1280BB12C0A2 6C1980CEFCB0007FBA1280BB12C0A26C1980422C7BAE4D>17 D<19E0F003F0180FF03FE0 F0FF80943803FE00EF0FF8EF3FE0EFFF80DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FC ED1FF8ED7FE0913801FF80DA07FEC9FCEC1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC048 48CBFCEA07FCEA1FF0EA7FC048CCFCA2EA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB 07FCEB01FF9038007FC0EC1FF0EC07FC913801FF809138007FE0ED1FF8ED07FE923800FF 80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF0FF8EF03FE943800FF80F03FE0F00FF018 03F000E01900B0007FB912E0BA12F0A26C18E03C4E78BE4D>20 D<127012FCB4FCEA7FC0 EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01FF9038007FC0EC1FF0EC07FC913801 FF809138007FE0ED1FF8ED07FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FE0EF 0FF8EF03FE943800FF80F03FE0F00FF0A2F03FE0F0FF80943803FE00EF0FF8EF3FE0EFFF 80DC03FEC7FCEE0FF8EE3FE0EEFF80DB03FEC8FCED1FF8ED7FE0913801FF80DA07FEC9FC EC1FF0EC7FC04948CAFCEB07FCEB1FF0EB7FC04848CBFCEA07FCEA1FF0EA7FC048CCFC12 FC1270CDFCB0007FB912E0BA12F0A26C18E03C4E78BE4D>I32 D<1AF0A3861A78A21A7C1A3CA2 1A3E1A1E1A1F747EA2747E747E87747E747E1B7E87757EF30FE0F303F8007FBC12FEBE12 80A26CF3FE00CEEA03F8F30FE0F31F8051C7FC1B7E63505A505A63505A505AA250C8FC1A 1E1A3E1A3CA21A7C1A78A21AF862A359347BB264>I<49B4EF3FC0010F01E0923803FFF8 013F01FC030F13FE4901FF92383FE01F48B66C91397E0007C02603F80301E0D901F8EB01 E02807E0007FF049486D7E01806D6CD907C0147048C76C6C494880001EDA07FE49C87E00 1C6E6C013E150C486E6D48150E71481506486E01E0160793387FF1F0006092263FF3E081 93381FFBC000E004FF1780486F4915017090C9FC82707F8482717E844D7E6C4B6D150300 6004EF1700933803E7FE0070922607C7FF5DDC0F837F003004816D140E00384BC6FC0018 033E6D6C5C001C4B6D6C143C6C4BD91FFC5C6C4A486D6C5C6DD907E06D6C13036C6C4948 6D9038E00FE0D801F0013FC890B55A27007C03FE6F91C7FC90263FFFF8031F5B010F01E0 030313F8D901FECAEA7FC0592D7BAB64>49 D<92B6FC02071580143F91B7120001030180 C8FCD907FCC9FCEB1FE0EB3F80017ECAFC5B485A485A485A5B485A121F90CBFC123EA212 3C127CA2127812F8A25AA2B9FC1880A2180000F0CBFCA27EA21278127CA2123C123EA27E 7F120F6C7E7F6C7E6C7E6C7E137E6D7EEB1FE0EB07FC6DB47E010090B6FC023F15801407 02001500313A78B542>I<1706170F171FA2173EA2177CA217F8A2EE01F0A2EE03E0A2EE 07C0A2EE0F80A2EE1F00A2163EA25EA25EA24B5AA24B5AA24B5AA24B5AA24BC7FCA2153E A25DA25DA24A5AA24A5AA24A5AA24A5AA24AC8FCA2143EA25CA25CA2495AA2495AA2495A A2495AA249C9FCA2133EA25BA25BA2485AA2485AA2485AA2485AA248CAFCA2123EA25AA2 5AA25A1260305C72C600>54 D<4B7E4B7EA21507A25EECFF8F010313EF90260F80FFC7FC 90383E003F497F49804848804848497E5B0007EC3DF049133C000FEC7CF8A248C7EA787C 15F848157E15F0A2140148157F007E4A7E1403A215C0A200FE01071480A21580140FA215 00A25CA2141E143EA2143CA2147CA21478A214F8A25C1301A2007E491400A21303A2007F 495B1307003F157E5CA2130F001F157C018FC712FCD80F9F5CA201DE130100075DD803FE 495AA26C48495A00004A5A017C49C7FC017E133E90387F80F89038FBFFE001F8138049C9 FC1201A25BA26C5A29557CCC32>59 D<0307B712C04AB8FC020F1780023F170049B812FC 4917F0D90FFCC700FCC8FCD91F80495A49C71203017E4A5A13FE00014B5A5B48484A5A13 E049143F0002C85BC9127FA294C9FC5EA34B5AA35E1503A34B5AA44B5AA44B5AA44B5AA3 5E157FA293CAFC5DA25D14015DA24A4814074B141F02075D4B147E4A485C4A48495A92C7 5B48B85A000F17804894C8FC4816FC4816E0B8C9FC424483C336>73 D<031FB512FC0203B712E0021F16FC91B9FC010318C0010F8490283FF07FC00380D9FE00 EC001FD801F804037FD803E04A13004848EF3FFC000F181F4848170F003F14FF007F1807 90C7FC00FE92C8FC486112F012C0C7485F190F4B5E62191F6202034CC7FC4B157E197C61 4E5A4A48EC07E0F00F80063FC8FCEF03FC4A4848B45A040F13E04C13804C48C9FC4A4848 7EA2041F7FEDC007023F6D7F824B6C7F147F717E92C7FC4A6E7EA24A141F010182170F4A 8101031907716C141F4A183E01076F6D137C4A18F8719038C001F0010F9438E003E04A6E 9038F007C0011F9438FC1F804A92397FFFFE006249486F13F091C96C13C0017C7048C7FC 0170EE03F050467EC354>82 D<0060170C00F0171EB3B3A66C173EA20078173C007C177C 007E17FC003E17F86CEE01F06D15036C6CED07E06C6CED0FC0D803F8ED3F80D801FEEDFF 0026007FC0EB07FCD93FFCEB7FF8010FB612E001031580D9007F01FCC7FC020713C0373D 7BBA42>91 D<913807FFC0027F13FC0103B67E010F15E0903A3FFC007FF8D97FC0EB07FC D801FEC8B4FCD803F8ED3F80D807E0ED0FC04848ED07E04848ED03F090C91201003EEE00 F8007E17FC007C177C0078173C00F8173EA248171EB3B3A60060170C373D7BBA42>I<15 38157CA215FEA24A7EA215EF02037FA2913807C7C0A291380F83E0A291381F01F0A2EC1E 00023E7FA24A137CA24A7FA249487FA24A7F010381A249486D7EA249486D7EA249C76C7E A2011E1400013E81A249157CA24981A2484881A24848ED0F80A2491507000717C0A24848 ED03E0A248C9EA01F0A2003EEE00F8A2003C1778007C177CA248173EA248171E0060170C 373D7BBA42>94 D102 D<12FEEAFFE0EA07F8EA00FEEB7F806D7E6D7E130F6D7EA26D7EB3AD6D7EA26D 7E806E7E6E7EEC0FE0EC03FC913800FFE0A2913803FC00EC0FE0EC3FC04A5A4AC7FC5C49 5AA2495AB3AD495AA2495A131F495A495A01FEC8FCEA07F8EAFFE048C9FC236479CA32> I<126012F0B3B3B3B3B3A81260046474CA1C>106 D<126012F07EA21278127CA2123C12 3EA2121E121FA26C7EA212077FA212037FA212017FA26C7EA21378137CA2133C133EA213 1E131FA26D7EA2130780A2130380A2130180A26D7EA21478147CA2143C143EA280A28081 A2140781A2140381A26E7EA2140081A21578157CA2153C153EA281A2811680A2150716C0 A2150316E0A2ED01F0A2150016F8A21678167CA2163C163EA2161E160C27647BCA32> 110 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Ft cmmi8 8 37 /Ft 37 120 df11 D<157E913801FFC091380781E091381E00F01438 4A13F84A1378495A494813F891C7FC5B1306010E1301010C14F0131C0118EB03E0ED07C0 013814809039301FEF00EC3FFE13709038601FEF9138000F80ED07C013E04914E0A31201 5BA30003140F90C713C0A348EC1F80A2ED3F00A2486C137E000D147C6D5B390CE001F039 1C7003E039183C0F80D91FFEC7FCEB03F80038C9FC1230A312701260A312E05AA3253C7E AE28>I<131FD9FFC013304801F0137000076D13604815E0D9807C13C0391E003C014801 1E13800038EB0E03480107130000605CEC030612E0C7138EEC018C159C159815B815B0A2 15F05DA35DA25DA21403A44AC7FCA4140EA45CA31418242C7F9D24>I<13E0486C133C15 FF00031303EC0F7F9038E01C7EEC381C000749C7FC5CEBC3C001C7C8FCEA0FDE13F8EBFF 8014F8381F83FEEB803F496C7E140F48154016C0123EA2007E14811680007C1403ED8300 00FC1487EC078E48EB03FC0070EB00F0221F7D9D29>20 D<13FC13FFEB1FC0130F6D7EA3 6D7EA2130180A26D7EA3147EA280A36E7EA2140F81A24A7E143F147FECF3F0EB01E3EB03 C190380781F8130F49C67E133E5B49137E485A48487F1207485A4848EB1F8048C7FC127E 48EC0FC048EC07E000701403232F7DAD29>I<131C013EEB0380ED07C0017E130F168013 7CA201FC131F16005BA200015C153E5BA20003147E157C5BA20007ECFC08EDF8185BA200 0F0101133816309038E003F002071370001F90380EF8609039F83C78E090397FF03FC090 391FC00F0048C9FCA2123EA2127EA2127CA212FCA25AA21270252C7E9D2A>I<90B612F8 12035A4815F03A1E0380C000003C130000701301130700E05CEAC00638000E03A3131CA2 133C140713381378A201F07FA21201A2D803E07FA20007130313C0A26C486C5A251E7E9C 29>25 DI<1506A3150E150CA3151C1518A315381530A31570D801E0EB6007D807 F8EC1F80EA0E3CD81C3E01E013C0003814C00030150F0070150726607E011480D8E07CEB 800312C013FC3880F803000002001300120113F04A5B00030106130601E0140E160C020E 131C020C131801C0143801E05C021C5B91381801C0D801F0495A030FC7FC3900FC381C90 383F30F890380FFFE0010190C8FCEB00701460A314E05CA313015CA42A3C7EAD2E>32 D<160E486C143F120348C813801206000E151F000C150F001C160000188112380030130C 141E007015061260143E023C130E00E0150C5A0238131C6C01785B14705E02F013F06C48 6C485A010313033A7C0FFC0FC03A7FFFBFFF80023F90C7FC393FFC1FFE391FF80FF83907 E007E0291F7F9D2C>II39 D<123C127E12FFA4127E123C08 087A8714>58 D<123C127EB4FCA21380A2127F123D1201A312031300A25A1206120E5A5A 5A126009157A8714>I<15C0140114031580A214071500A25C140EA2141E141CA2143C14 3814781470A214F05CA213015CA213035C130791C7FCA25B130EA2131E131CA2133C1338 A21378137013F05BA212015BA212035BA2120790C8FC5A120EA2121E121CA2123C1238A2 12781270A212F05AA21A437CB123>61 D<92387FC003913903FFF80791391FC03E0F9139 7E00071FD901F8EB03BF4948EB01FED90FC013004948147E49C8FC017E157C49153C485A 120348481538485AA2485A173048481500A2127F90CAFCA35A5AA292381FFFFCA2923800 3FC0EE1F80163F1700A2127E5E167E7EA26C6C14FE000F4A5A6C7E6C6C1307D801F8EB1E 3CD8007EEBFC3890391FFFE018010390C8FC302F7CAD37>71 D<90383FFFFCA2903800FE 00A25CA21301A25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA291C7FCA2 5BA2137EA213FEA25BA21201A25BA21203B512E0A21E2D7DAC1F>73 D77 D<3B7FFFF801FFFEA2D801 FCC7EA0FC0178049EC070016060003150E160C5BA20007151C16185BA2000F153816305B A2001F157016605BA2003F15E05E90C8FCA24814015E127EA2150300FE92C7FC5A5D1506 150E007C5C151815386C5C5D6CEB03C0260F800FC8FC3803E03C3801FFF038003FC02F2E 7BAC30>85 DI< 90260FFFFCEB7FFFA29026007FC0EB0FF06E48148018006E6C131E1718020F5C6F5B0207 5C6F485A020349C7FCEDF8065E6E6C5A5E6E6C5A5EED7F8093C8FC6F7EA26F7E153F156F EDCFE0EC018791380307F0EC0703020E7F141C4A6C7E14704A6C7E495A4948137F49C7FC 010E6E7E5B496E7E5BD801F081D807F8143FD8FFFE0103B5FCA2382D7EAC3A>88 DI<01 07B612F8A2903A0FFC0007F002E0EB0FE00280EB1FC049C71380011E143F011CEC7F0049 14FE4B5A0130495A0170495A0160495A4B5A4B5A90C748C7FCA215FE4A5A4A5A4A5A4A5A 4A5A4A5A4AC8FC14FE5C130149481306495A4948130E4948130C495A49C7121C01FE1418 48481438485A5E484814F048481301484813034848495A48C7127FB7FC5E2D2D7CAC30> I99 D<14FCEB03FF90380F839C90381F01BC013E13FC EB7C005B1201485A15F8485A1401120F01C013F0A21403121F018013E0A21407A215C0A2 000F130F141F0007EB3F80EBC07F3803E1FF3800FF9F90383E1F0013005CA2143EA2147E 0038137C00FC13FC5C495A38F807E038F00F80D87FFEC7FCEA1FF81E2C7E9D22>103 D<1307EB0F80EB1FC0A2EB0F80EB070090C7FCA9EA01E0EA07F8EA0E3CEA1C3E12381230 1270EA607EEAE07C12C013FC485A120012015B12035BA21207EBC04014C0120F13801381 381F01801303EB0700EA0F06131EEA07F8EA01F0122E7EAC18>105 D<15E0EC01F01403A3EC01C091C7FCA9147CEB03FE9038078F80EB0E07131C013813C013 30EB700F0160138013E013C0EB801F13001500A25CA2143EA2147EA2147CA214FCA25CA2 1301A25CA21303A25CA2130700385BEAFC0F5C49C7FCEAF83EEAF0F8EA7FF0EA1F801C3B 81AC1D>I<131FEA03FFA2EA003FA2133EA2137EA2137CA213FCA25BA2120115F89038F0 03FCEC0F0E0003EB1C1EEC387EEBE07014E03807E1C09038E3803849C7FC13CEEA0FDC13 F8A2EBFF80381F9FE0EB83F0EB01F81300481404150C123EA2007E141C1518007CEBF038 ECF83000FC1470EC78E048EB3FC00070EB0F801F2F7DAD25>I<137CEA0FFCA21200A213 F8A21201A213F0A21203A213E0A21207A213C0A2120FA21380A2121FA21300A25AA2123E A2127EA2127CA2EAFC08131812F8A21338133012F01370EAF860EA78E0EA3FC0EA0F000E 2F7DAD15>I<27078007F0137E3C1FE01FFC03FF803C18F0781F0783E03B3878E00F1E01 263079C001B87F26707F8013B00060010013F001FE14E000E015C0485A4914800081021F 130300015F491400A200034A13076049133E170F0007027EEC8080188149017C131F1801 000F02FCEB3F03053E130049495C180E001F0101EC1E0C183C010049EB0FF0000E6D48EB 03E0391F7E9D3E>I<3907C007E0391FE03FF83918F8783E393879E01E39307B801F3870 7F00126013FEEAE0FC12C05B00815C0001143E5BA20003147E157C5B15FC0007ECF80816 18EBC00115F0000F1538913803E0300180147016E0001F010113C015E390C7EAFF00000E 143E251F7E9D2B>I<90387C01F89038FE07FE3901CF8E0F3A03879C0780D907B813C000 0713F000069038E003E0EB0FC0000E1380120CA2D8081F130712001400A249130F16C013 3EA2017EEB1F80A2017C14005D01FC133E5D15FC6D485A3901FF03E09038FB87C0D9F1FF C7FCEBF0FC000390C8FCA25BA21207A25BA2120FA2EAFFFCA2232B829D24>112 D<903807E03090381FF87090387C1CF0EBF80D3801F00F3903E007E0EA07C0000F130338 1F800715C0EA3F00A248130F007E1480A300FE131F481400A35C143E5A147E007C13FE5C 1301EA3E07EA1F0E380FFCF8EA03F0C7FC13015CA313035CA21307A2EBFFFEA21C2B7D9D 20>I<3807C01F390FF07FC0391CF8E0E0383879C138307B8738707F07EA607E13FC00E0 EB03804848C7FCA2128112015BA21203A25BA21207A25BA2120FA25BA2121FA290C8FC12 0E1B1F7E9D20>I<130E131FA25BA2133EA2137EA2137CA213FCA2B512F8A23801F800A2 5BA21203A25BA21207A25BA2120FA25BA2001F1310143013001470146014E0381E01C0EB 0380381F0700EA0F0EEA07FCEA01F0152B7EA919>116 D118 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fu cmti12 12 59 /Fu 59 128 df<4CB414FC040F9039C003FF80933B3F81F00783C0933B7C00781F01E04C 9038F83F03923C01F001FC3E07F003030103EB7E0F922607E007EB7C1F19FCDB0FC001F8 14E0943A03F0F80FC0DD01E1EB0780031FD9000190C7FC5E180361153F93C7FCA2180761 5D157EA2180F6115FE91B912F0A3DA00FCC7D81F80C7FC1401A25D183F96C8FCA214035D A260187E14075DA218FE60140F5DA2170160141F5DA2170360143F92C7FCA21707605C14 7EA2170F6014FE5CA24D5AA2495A95C9FC5F5C0103153E177E001CEBE038007F02FE137C 26FF07E114FC02C15C4C5AEB0F8100FE903901FC03E0D8F81F9038F007C03B701E00E00F 80D8783CD9F83ECAFCD81FF0EB3FF8D807C0EB0FE04C5A83C53C>11 DI<123C127C12FE A27E7EEA3F80121F13C0120FEA07E0120313F0120112001378A2133813100D1364C432> 18 DI<13F0EA03F8EA07FC120FA6EA03CCEA001C13 18A213381330A2137013E013C0120113801203EA0700120E5A5A5A5A5A0E1D6BC41E>39 D<167016E0ED01C0ED0380ED0700150E153C5D15F85D4A5A4A5A4A5A140F4AC7FC141E14 3E5C147814F8495A5C1303495AA2495AA249C8FCA25B133E137E137CA25BA212015BA212 035BA212075BA2120FA25BA2121FA290C9FCA25AA2123EA3127EA2127CA65AAB1278A612 7C123CA47EA2120E120FA27E6C7EA26C7EA26C7E1360246472CA28>I<1560A2157081A2 81151E150E150FA2811680A3ED03C0A516E0A21501A71503A91507A216C0A4150FA21680 A2151FA21600A25DA2153EA2157EA2157C15FCA25D1401A25D14035DA214075D140F5DA2 4AC7FCA2143EA25C147814F8495AA2495A5C1307495A91C8FC131E133E5B13785B485A48 5A485A48C9FC121E5A5A12E05A23647FCA28>I<13F0EA03FC1207A2EA0FFEA4EA07FCEA 03CCEA000C131C1318A2133813301370136013E0EA01C013801203EA0700120E5A5A5A5A 5A0F1D7A891E>44 D<007FB5FCB6FCA214FEA21805789723>I<120FEA3FC0127FA212FF A31380EA7F00123C0A0A76891E>I<16C01501A215031507ED0F80151F153F157F913801 FF005C140F147F903807FCFEEB0FF0EB0700EB00015DA314035DA314075DA3140F5DA314 1F5DA3143F5DA3147F92C7FCA35C5CA313015CA313035CA313075CA2130FA2131F133FB6 12FCA25D224276C132>49 DII<130FEB1FC0133FEB7FE013FFA214C0EB7F801400131E 90C7FCB3A5120FEA3FC0127FA212FFA35B6CC7FC123C132B76AA1E>58 D65 D67 D<91B712F818FF19C00201903980003FF06E90C7EA0FF84AED03FCF000FE4B157FA2F13F 800203EE1FC05DF10FE0A214074B16F01907A2140F5D1AF8A2141F5DA2190F143F5D1AF0 A2147F4B151FA302FF17E092C9123FA34918C04A167F1A80A2010317FF4A1700A24E5A13 074A4B5A611807010F5F4A4B5A181F61011F4C5A4A4BC7FC18FE4D5A013F4B5A4A4A5A4D 5A017FED3FC005FFC8FC4AEB03FE01FFEC1FF8B812E094C9FC16F845447AC34A>I<91B9 12C0A30201902680000313806E90C8127F4A163F191F4B150FA30203EE07005DA314074B 5D190EA2140F4B1307A25F021F020E90C7FC5DA2171E023F141C4B133C177C17FC027FEB 03F892B5FCA39139FF8003F0ED00011600A2495D5CA2160101034B13705C19F061010791 C8FC4A1501611803010F5F4A150796C7FC60131F4A151E183E183C013F167C4A15FC4D5A 017F1503EF0FF04A143F01FF913803FFE0B9FCA26042447AC342>I<91B91280A3020190 2680000713006E90C8FC4A163FA24B81A30203160E5DA314074B151E191CA2140F5D1707 5F021F020E90C7FC5DA2171E023F141C4B133CA2177C027F5CED800392B5FCA291B65AED 00071601A2496E5A5CA2160101035D5CA2160301075D4A90CAFCA3130F5CA3131F5CA313 3F5CA2137FA313FFB612E0A341447AC340>II<027FB512E091B6FCA20200EBE000ED7F8015FF A293C7FCA35C5DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C8 FCA35B5CA313035CA313075CA3130F5CA3131F5CA2133FA25CEBFFE0B612E0A25D2B447B C326>73 D<91B66C90383FFFF8A302010180C7000F13006E90C8EA07FC4A17F01AC04B4B 5A4FC7FC193C02035E4B5DF003E0F0078002074BC8FC4B141E6018F8020F4A5A4BEB03C0 4D5A4DC9FC021F141E4B137C17F04C5A023F495A4B487E161F163F027F497EED80FFED81 EF923883CFF89138FF8F8FED1E07033C7F157849EBF00303E07F15C092380001FF495A5C 707FA213074A6E7EA2173F010F825C171F84131F4A140F84A2013F6F7E5CA2017F6F7EA2 4A4A7E496C4A7FB66C90B512FC5E614D447AC34B>75 D<91B612F0A25F020101C0C7FC6E 5B4A90C8FCA25DA314035DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92C9 FCA35B5CA3010316104A1538A21878010716705C18F018E0010F15015C18C01703011F15 074A1580170FA2013FED1F004A5C5F017F15FE16034A130F01FFEC7FFCB8FCA25F35447A C33D>I<91B56C93387FFFC08298B5FC02014DEBC0006E614A5FA203DF4C6CC7FC1A0E63 912603CFE05D038F5F1A381A711407030FEEE1FCA2F101C3020FEE0383020E60F107036F 6C1507021E160E021C60191CF1380F143C023804705BA2F1E01F0278ED01C091267003F8 5EF003801A3F02F0ED070002E0030E5CA24E137F130102C04B91C8FC606201036D6C5B02 805F4D5A943803800113070200DA07005BA2050E1303495D010E606F6C5A1907011E5D01 1C4B5CA27048130F133C01384B5C017892C7FC191F01F85C486C027E5DD807FE027C4A7E B500F00178013FB512C0A216705A447AC357>I<91B56C49B512E0A28202009239000FFC 00F107F0706E5A4A5F15DF705D1907EC03CFDB8FF892C7FCA203875D02077F0303150EA2 70141EEC0F01020E161C826F153C141E021C6E1338167F1978023C800238013F1470A271 13F00278131F02705E83040F130102F014F84A5E1607EFFC0313014A01035C17FE180701 0314014A02FF90C8FCA2705B0107168F91C8138E177F18DE5B010EED3FDC18FCA2011E15 1F011C5EA2170F133C01386F5A1378A201F81503486C5EEA07FEB500F01401A2604B447A C348>II<91B712F018FEF0FF800201903980007FE06E90C7EA1FF04AED07F81803 4B15FCF001FE1403A24B15FFA21407A25DA2140FF003FE5DA2021F16FC18074B15F8180F 023F16F0F01FE04B15C0F03F80027FED7F0018FE4BEB03FCEF0FF002FFEC7FC092B6C7FC 17F892CAFC5BA25CA21303A25CA21307A25CA2130FA25CA2131FA25CA2133FA25CA2137F A25C497EB67EA340447AC342>I<91B77E18F818FE020190398001FF806E90C7EA3FC04A ED1FE0F00FF04BEC07F8180319FC14034B15FEA314075DA3020FED07FC5DA2F00FF8141F 4B15F0F01FE0F03FC0023F16804BEC7F0018FEEF03F8027F4A5A4BEB1FC04CB4C7FC92B5 12F891B612E092380003F8EE00FE177F496F7E4A6E7EA28413034A140FA2171F13075CA2 173F130F5CA24D5A131F5CA3013F170E5CA2017FEE801E191C4A163C496C1638B66C9038 3FC070051F13F094380FE1E0CA3803FF80943800FE003F467AC347>82 DI<48B912F85AA2913B0007FC 001FF0D807F84A130701E0010F140349160148485C90C71500A2001E021F15E05E121C12 3C0038143F4C1301007818C0127000F0147F485DA3C800FF91C7FC93C9FCA35C5DA31403 5DA314075DA3140F5DA3141F5DA3143F5DA3147F5DA314FF92CAFCA35B5CA21303A21307 497E007FB612C0A25E3D446FC346>I<001FB500F090383FFFFCA326003FF0C700011380 6D48913800FE00013F167C18785C187018F0017F5E5CA2170101FF5E91C8FCA21703485F 5BA21707000394C7FC5BA25F0007160E5BA2171E120F49151CA2173C121F491538A21778 123F491570A217F0127F495DA2160100FF5E90C8FCA216035F16074893C8FC5E160E161E 5E007E1538007F15785E6C4A5A6D495A001F4A5A6D49C9FC6C6C133E6C6C13F83903FC07 F0C6B512C0013F90CAFCEB07F83E466DC348>I87 D97 DIIIII<15FCEC03FF9139 0F83838091393E01CFC091387C00EF4A13FF4948137F010315804948133F495A131F4A14 00133F91C75A5B167E13FE16FE1201495CA215011203495CA21503A2495CA21507A25EA2 150F151F5E0001143F157F6C6C13FF913801DF8090387C039F90383E0F3FEB0FFCD903F0 90C7FC90C7FC5DA2157EA215FEA25DA2001C495A127F48495A14074A5A485C023FC8FC00 F8137E387C01F8381FFFE0000390C9FC2A407BAB2D>I<14FE137FA3EB01FC13001301A2 5CA21303A25CA21307A25CA2130FA25CA2131FA25C157F90393F83FFC091388F81F09138 1E00F802387F4948137C5C4A137EA2495A91C7FCA25B484814FE5E5BA2000314015E5BA2 000714035E5B1507000F5DA249130F5E001F1678031F1370491480A2003F023F13F0EE00 E090C7FC160148023E13C01603007E1680EE070000FEEC1E0FED1F1E48EC0FF80038EC03 E02D467AC432>I<143C147E14FE1301A3EB00FC14701400AE137C48B4FC3803C7803807 03C0000F13E0120E121C13071238A21278EA700F14C0131F00F0138012E0EA003F1400A2 5B137EA213FE5B12015BA212035B141E0007131C13E0A2000F133CEBC038A21478EB8070 14F014E0EB81C0EA0783EBC7803803FE00EA00F8174378C11E>I<16F0ED03F8A21507A3 16F0ED01C092C7FCAEEC01F0EC07FCEC1E1EEC380F0270138014E0130114C0EB03800107 131F1400A2130E153F131E011C140090C7FC5DA2157EA215FEA25DA21401A25DA21403A2 5DA21407A25DA2140FA25DA2141FA25DA2143FA292C7FCA25C147EA214FE001C5B127F48 485A495AA248485A495AD8F81FC8FCEA707EEA3FF8EA0FC0255683C11E>I<14FE137FA3 EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C167E013F49B4FC 92380783C09138000E07ED3C1F491370ED603F017E13E0EC01C09026FE03801380913907 000E00D9FC0E90C7FC5C00015B5C495AEBF9C03803FB8001FFC9FCA214F03807F3FCEBF0 7F9038E01FC06E7E000F130781EBC003A2001F150FA20180140EA2003F151E161C010013 E0A2485DA2007E1578167000FE01015B15F1489038007F800038021FC7FC2A467AC42D> IIIIII<91381F800C91387FE01C903901F0703C903907C0387890390F 801CF890381F001D013E130F017E14F05B48481307A2484814E012075B000F140F16C048 5AA2003F141F491480A3007F143F90C71300A35D00FE147EA315FE5DA2007E1301A24A5A 1407003E130FA26C495A143B380F80F33807C3E73901FF87E038007E071300140F5DA314 1F5DA3143F92C7FCA25CA25C017F13FEA25D263F76AB2D>III<1470EB01F8A313035CA313075CA3130F5CA3 131F5CA2007FB512E0B6FC15C0D8003FC7FCA25B137EA313FE5BA312015BA312035BA312 075BA3120F5BA2EC0780001F140013805C140E003F131EEB001C143C14385C6C13F0495A 6C485AEB8780D807FEC7FCEA01F81B3F78BD20>I<137C48B414072603C780EB1F803807 03C0000F7F000E153F121C0107150012385E1278D8700F147E5C011F14FE00F05B00E05D EA003FEC0001A2495C137E150313FE495CA215071201495CA2030F13380003167849ECC0 70A3031F13F0EE80E0153F00011581037F13C06DEBEF8300000101148090397C03C78790 3A3E0F07C70090391FFE01FE903903F000782D2D78AB34>I<017C143848B414FC3A03C7 8001FE380703C0000F13E0120E001C14000107147E1238163E1278D8700F141E5C131F00 F049131C12E0EA003F91C7123C16385B137E167801FE14705BA216F0000115E05B150116 C0A24848EB0380A2ED0700A2150E12015D6D5B000014786D5B90387C01E090383F0780D9 0FFFC7FCEB03F8272D78AB2D>I<017CEE038048B4020EEB0FC02603C780013FEB1FE038 0703C0000E7F5E001C037E130F01071607123804FE130300785DEA700F4A1501011F1301 00F001804914C012E0EA003FDA000314034C14805B137E0307140701FE1700495CA2030F 5C0001170E495CA260A24848495A60A2601201033F5C7F4B6C485A000002F713036D9039 E7E0078090267E01C349C7FC903A1F0781F81E903A0FFF007FF8D901FCEB0FE03B2D78AB 41>I<02F8133FD907FEEBFFE0903A0F0F83C0F0903A1C07C780F890393803CF03017013 EE01E0EBFC07120101C013F8000316F00180EC01C000074AC7FC13001407485C120EC7FC 140F5DA3141F5DA3143F92C8FCA34AEB03C01780147EA202FEEB0700121E003F5D267F81 FC130E6E5BD8FF83143CD903BE5B26FE079E5B3A7C0F1F01E03A3C1E0F83C0271FF803FF C7FC3907E000FC2D2D7CAB2D>I<137C48B414072603C780EB1F80380703C0000F7F000E 153F001C1600130712385E0078157EEA700F5C011F14FE00F0495B12E0EA003FEC00015E 5B137E150301FE5C5BA2150700015D5BA2150F00035D5BA2151F5EA2153F12014BC7FC6D 5B00005BEB7C0390383E0F7EEB1FFEEB03F090C712FE5DA214015D121F397F8003F0A24A 5A4848485A5D48131F00F049C8FC0070137E007813F8383801F0381E07C06CB4C9FCEA01 FC294078AB2F>I<027C130749B4130F49EB800E010F141E49EBC03CEDE03890393F03F0 7890397C00FDF00178EB3FE00170EB03C001F0148049130790C7EA0F00151E5D5D5D4A5A 4A5A4A5A4AC7FC141E5C5C5C495A495A495A49C8FC011E14F04914E05B491301485A4848 EB03C0D807B0130701FEEB0F80390FCF801F3A1F07E07F00393E03FFFED83C015B486C5B 00705C00F0EB7FC048011FC7FC282D7BAB28>I<000FEB0780393F801FC0397FC03FE000 FF137FA4018013C0397F003F80003CEB1E001B0A66C232>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fv cmmi12 12 65 /Fv 65 123 df11 DI< EB01FCD907FF15E0011F13C0017F6DEB01C090B56C1480486E13032603FE0715002707F0 00FC5B01C0017C130648C76C130E001E021E130C001C80003C6E131C00381618486E1338 EE8030006002011370176000E016E0C86D5A150016C15F16C394C7FC16E316E71666166E 166CA2167C1678A3167016F05EA35EA31501A25E1503A44BC8FCA35D150EA45DA45DA333 417EAB33>I<1578913807FFE0021F13FC91383C7FFEEC7007EC6003ECE0004A13381600 A280A380A280147CA2147E143E143F816E7EA26E7E81140781EC3FFC14FF903803E1FEEB 07C190381F00FF133E49EB7F805B0001143F485A484814C049131F120F485AA248C7FC15 0F5A127EA300FEEC1F805AA316005A5DA2153E157E157CA26C5C127C4A5A6C495AA26C49 5A6C6C485A6C6C48C7FC3803E07C3800FFF0EB1FC027487CC62B>I<01F8EB03FCD803FE EB1FFFD8071F90387C0FC03B0E0F80E007E0001C9038C3C003271807C70013F002CE1301 003801DC14F8003013D8EB0FF800705B00605BA200E0491303D8C01F15F05C1200160713 3F91C713E0A2160F5B017E15C0A2161F13FE491580A2163F1201491500A25E120349147E A216FE1207495CA21501120F495CEA0380C81203A25EA21507A25EA2150FA25EA2151FA2 5EA2153FA293C7FC150E2D417DAB30>17 D<130E011FEC03E049EC1FF8167F16E749EB03 C792380707F0017E130E92381C03C001FE0178C7FC15E049485A4A5A000149C8FC141EEB F8385C3803F9E0EBFF8014F8ECFFC03907F07FF0EC03FC49C6B4FCED3F80000F6E7EA249 130FA2001F160717065BA2003F160E170C90C71380171C4816181738007E1630923807C0 7000FE16E0923803E1C048913800FF800038ED3E00302D7BAB38>20 DI<147002F8140E0101153FA301035DA24A147EA2010715FEA24A5CA2010F1401A24A 5CA2011F1403A24A5CA2013F1407A291C75BA249140FA2017E5DA201FE021F1318183849 ED8030A20001033F13701860EE7F005E486C16E0DB01DF13C09238039F016DD9071F1380 489039801E0F83903BF7C078078700903AE1FFE003FE903AE07F8000F8000F90CAFCA25B A2121FA25BA2123FA290CBFCA25AA2127EA212FEA25A123835417DAB3B>I<010FB712E0 013F16F05B48B812E04817C02807E0060030C7FCEB800EEA0F00001E010C13705A003801 1C13605A0060011813E000E013381240C7FC5C4B5AA214F014E01301150314C01303A3EB 078082130FA2EB1F00A34980133E137EA24980A2000114015BA26C48EB00E0342C7EAA37 >25 DI<0203B612E002 1F15F091B7FC4916E0010716C090270FF80FF8C7FC90381FC00349486C7E017EC7FC4914 7E485A4848143E0007153F5B485AA2485AA2123F90C8FC5E48157E127EA216FE00FE5D5A 15015EA24B5A007C5D15074B5A5E6C4AC8FC153E6C5C5D390F8003F03907C007C02601F0 3FC9FC38007FFCEB1FE0342C7DAA37>I<1730A317701760A317E05FA316015FA3160394 C8FCA35E1606A3160E160C013E1607D9FF80ED1F802603C3C0011CEB3FC0260703E01318 260601F0157F000E173F001C1538D818030230131F0038170F0030170700701570D86007 026013035CA2D8E00F02E0148000C049491301EA001F4A150303011500013F5C14006049 01031406017E91C7FC180E180C01FE49141C4901061418183860030E1460030C14E04D5A 4D5A031C49C7FC0318130E017E5D5F6D01385B90261F80305BD90FC0EB03C0D907F0010F C8FC903901FE707C9039003FFFF002031380DA0060C9FC15E05DA314015DA3140392CAFC A35C1406A3140E140C3A597DC43F>32 D<180E0118163F0138EE7F805B016016FF01E016 7F485A49163F0003171F90CAFC48170F1206000E1707120C1900001C14060018140FA200 38021E14061230A2180E00704A140C1260181C181803381438157800E002705CA203F05C 6C010114014D5A14030078496C495A020F141F007CD91F7C49C7FC007ED97E7E137E3B7F 83FE7F03FC6CB4486CB45A02F85C6C496C5B6C01C05C6CD9000790C8FCD801FCEB01F839 2D7FAB3D>II<177F01 30913803FFC00170020F13E0494A13F048484A13F84848EC7F0190C838F8007C484A4813 3C00064A48131C000E4B131E000C4A48130E001C92C7FC0018140E150C0038021C140600 3014185D180E00704A140C1260154003C0141C00E017184A5A4817386C17304AC8127018 E01260007049EC01C0EF03800078010614070038EE0F00003C010E141E6C167CD81F805D 6C6C48EB03F0D807F0EC0FE0D803FEEC3FC02801FFFC03FFC7FC6C6CB55A6D14F8010F14 E0010114809026007FF8C8FC02F8C9FCA25CA21301A3495AA31307A25C130FA4131F5C6D CAFC37417BAB40>39 D<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>58 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A312011380120313005A 1206120E5A5A5A12600B1D78891B>II<1618163C16 7CA2167816F8A216F01501A216E01503A216C01507A21680150FA2ED1F00A2151E153EA2 153C157CA2157815F8A25D1401A24A5AA25D1407A25D140FA292C7FC5CA2141E143EA214 3C147CA25CA25C1301A25C1303A25C1307A25C130FA291C8FC5BA2133EA2133C137CA213 7813F8A25B1201A25B1203A2485AA25B120FA290C9FC5AA2121E123EA2123C127CA21278 12F8A25A126026647BCA31>I<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB 1FF0EB07FE903801FF809038007FE0EC1FF8EC03FE913800FF80ED3FE0ED0FF8ED03FF03 0013C0EE3FF0EE0FFCEE01FF9338007FC0EF1FF0EF07FCEF01FF9438007FC0F01FE0A2F0 7FC0943801FF00EF07FCEF1FF0EF7FC04C48C7FCEE0FFCEE3FF0EEFFC0030390C8FCED0F F8ED3FE0EDFF80DA03FEC9FCEC1FF8EC7FE0903801FF80D907FECAFCEB1FF0EB7FC04848 CBFCEA07FCEA1FF0EA7FC048CCFC12FC12703B3878B44C>I64 D<1830187018F0A217011703A24D 7EA2170F171FA21737A2176717E717C793380187FCA2EE0307EE07031606160CA2161816 38163004607FA216C0030113011680ED0300A21506150E150C5D845D03707F15605DA24A 5A4AB7FCA25C0206C87F5C021C157F14185CA25C14E05C495A8549C9FC49163F1306130E 5B133C137C01FE4C7ED807FFED01FF007F01F0027FEBFFC0B5FC5C42477DC649>I<91B8 7E19F019FC02009039C00003FF6F480100138003FFED3FC01AE093C8121FF10FF0A24A17 F84B1507A314035D190FA2020717F04B151F1AE0193F020F17C04BED7F80F1FF004E5A02 1F4B5A4B4A5AF01FF0F03FC0023F4AB4C7FC4BEB1FFC92B612F018FEDA7FC0C7EA7F804B EC1FC0F00FF0727E02FF6F7E92C8FC727EA249835CA313035CA301075F4A1503A24E5A13 0F4A4B5A4E5AA2011F4C5A4A4B5A4D485A013F4B48C7FCEF0FFC4AEC3FF801FF913801FF E0B9128005FCC8FC17C045447CC34A>I<4CB46C1318043F01F013384BB512FC0307D900 7E1378DB1FF090380F80F0DB7F80EB03C1DA01FEC7EA01C34A48EC00E7DA0FF0ED7FE04A 48153F4A5A02FFC9121F494817C04948160F495A130F4A178049481607495A137F494817 0091CAFC5A485A1906485AA2485A96C7FC121F5BA2123F5BA3127F5BA4485AA419C0A218 0161127F180396C7FC6018066C6C160E601818001F17386D5E000F5F6D4B5A6C6C4B5A00 034CC8FC6C6C150E6C6C153C017F5DD93FC0EB01E0D91FF0EB0FC0D907FE017FC9FC0101 B512FCD9003F13E0020790CAFC45487CC546>I<91B87E19F019FC02009039C00007FF6F 489038007FC003FFED1FE0737E93C86C7E737E19014A707E5D1A7FA20203EF3F805DA21B C014075DA3140F4B17E0A3141F4B17C0A3143F4B167FA3027F18804B16FFA302FF180092 C95A62A24917034A5F19076201034D5A5C4F5A620107173F4A5F4FC7FC19FE010F4C5A4A 15034E5AF00FE0011F4C5A4A4B5A06FFC8FC013FED01FCEF0FF84AEC3FE001FF913803FF 80B848C9FC17F094CAFC4B447CC351>I<91B912FCA3020001C0C7123F6F48EC03F803FF 1501190093C91278A21A385C5DA3020317305DA314074B1460A218E0020F4B13005DA217 01021F5D4B13031707170F023F027FC8FC92B6FCA391397FC0007E4B131EA2170E02FF14 0C92C7FCA2171C49031813035C611906010392C7FC4A160E190C191C010717184A163819 301970130F4A5E180161011F16034A15074E5A013F163F4EC7FC4AEC03FF01FFED3FFEB9 FCA26046447CC348>I<91B912F8A3020001C0C7123F6F48EC07F003FF1503190193C9FC A21A705C5DA3020317605DA314075D18C01701020F4B13005DA21703021F92C8FC4B5BA2 5F023F141E4B13FE92B5FCA24A5CED8000173CA202FF141892C7FCA217384915305CA217 70010315604A91C9FCA313075CA3130F5CA3131F5CA2133FA313FFB612F8A345447CC33F >I<4CB46C1318043F01F013384BB512FC0307D9007E1378DB1FF090380F80F0DB7F80EB 03C1DA01FEC7EA01C34A48EC00E7DA0FF0ED7FE04A48153F4A5A02FFC9121F494817C049 48160F495A130F4A178049481607495A137F4948170091CAFC5A485A1906485AA2485A96 C7FC121F5BA2123F5BA3127F5BA4485A4CB612805EA293C7EBE000725AA3007F60A218FF 96C7FCA26C7E5F606C7EA2000F16036D5E6C6C15070003160F6C6C151F6C6CED3DF8D97F 8014786D6CEB01E0D91FF0903807C078D907FE90387F00700101B500FC1330D9003F01F0 90C8FC020790CAFC45487CC54D>I<91B6D8E003B61280A3020001E0C70003EB8000DB7F 806E48C7FC03FF1503A293C85BA219075C4B5EA2190F14034B5EA2191F14074B5EA2193F 140F4B5EA2197F141F4B5EA219FF143F92B8C8FCA3DA7FC0C712014B5DA2180314FF92C8 5BA218075B4A5EA2180F13034A5EA2181F13074A5EA2183F130F4A5EA2187F131F4A5EA2 013F16FFA24A93C9FCD9FFE002037FB6D8E003B67EA351447CC351>I<027FB512F8A217 F09139007FF000ED3FC0157FA25EA315FF93C7FCA35C5DA314035DA314075DA3140F5DA3 141F5DA3143F5DA3147F5DA314FF92C8FCA35B5CA313035CA313075CA3130F5CA2131FA2 5CEB7FF0007FB512F0B6FCA22D447DC32B>I<91B600E049B512C0A3020001E0C8383FF8 00DB7F80ED1FE003FF94C7FC1A3E93C9127862F101C04A4C5A4B4BC8FC191C6102035E4B 5DF003804EC9FC0207150E4B14386060020F4A5A4B0107CAFC170E5F021F14784B13F84C 7E1603023F130F4B487E163BEEE1FF91387FC1C1DB83807FED8700159CDAFFB86D7E5D03 C06D7E5D4990C7FC4A6E7EA2717E13034A811707A201076F7E5C717EA2130F4A6E7FA272 7E131F5C727E133F854A82D9FFE04B7EB600E0010FB512E05FA252447CC353>75 D<91B612F8A3020001E0C8FC6F5A4B5AA293C9FCA35C5DA314035DA314075DA3140F5DA3 141F5DA3143F5DA3147F5DA314FF92CAFCA35B4A16C0A21801010317804A15031900A201 075E4A1506180E181E010F161C4A153C18381878011F16F84A4A5A1703013F150F4D5A4A 14FF01FF02075BB9FCA2603A447CC342>I<91B500C0933803FFFE63630200F1FE00DB6F E0EE1BF803EF171F1B3703CFEF67F0A21BCF0201EF018F038F60DB87F0ED030F1B1F0203 17060307040C5BA2F2183F020717300206616F6C15601B7F020E17C0020CDC018090C7FC A24F485A021C16060218606F6C5C1A0102381618023004305BA2F16003027016C0026060 6F6CEB01801A0702E0ED03004A03065CA24E130F01015E4A60047F5B1A1F01035E91C74A 5CA24D48133F494BC7FC010661EE3F861A7F010E158C010C039892C8FCA205B05C011C15 E001186001386E5A190101785D01FC92C75BD803FFEF07FEB500F8011E0107B512FE161C 160C5F447BC35E>I<91B712FEF0FFE019F802009039C0000FFE6F48EB01FF03FF913800 7F80F13FC093C8EA1FE0A24AEE0FF0A25D1AF81403A25DA21407F11FF05DA2020FEE3FE0 A24B16C0197F021F1780F1FF004B4A5A4E5A023F4B5A4E5A4BEC3FC006FFC7FC027FEC07 FC92B612F018800380CAFC14FFA292CBFCA25BA25CA21303A25CA21307A25CA2130FA25C A2131FA25CA2133FA25CEBFFE0B612E0A345447CC33F>80 DI<91B712F018FF19E002009039C0003FF86F48EB07FC03FFEC01FEF0007F 93C8EA3F801AC0F11FE05C5D1AF0A214035DA30207EE3FE05DA2F17FC0020F17804B15FF 1A004E5A021F4B5A4B4A5AF00FE04E5A023F037FC7FC4BEB03FCEF1FF092B612804A4AC8 FC923980007F80EF0FC0EF07F002FF6E7E92C77F1701845B4A1400A2170113035CA21703 13075CA24D5A130F5CA3011F18185CA2013F4C13381A304A6F1370D9FFE0020314E0B600 E0ED01C00501EB0380943900FE0F00CBEA3FFEF007F045467CC34A>I<9339FF80018003 07EBF003033F13FC9239FF007E07DA01F8EB0F0FDA07E09038079F004A486DB4FC4AC77E 023E804A5D187E5C495A183C495AA213074A1538A3130F183080A295C7FC806D7E8014FF 6D13E015FC6DEBFFC06D14FC6E13FF6E14C0020F80020314F8EC003F03077F9238007FFE 160F1603707E8283A283A21206A4000E163EA2120C177E001E167CA25F5F003F15014C5A 6D4A5A4C5A486C4AC8FC6D143ED87CF85CD8787E495A3AF01FC00FE0D8E007B512800101 49C9FC39C0003FF039487BC53C>I<48BA12C05AA291C7D980001380D807F092C7121F49 49150F0180170748C75B1903120E48020316005E12181238003014074C5C007018061260 00E0140F485DA3C8001F92C7FC5EA3153F5EA3157F5EA315FF93CAFCA35C5DA314035DA3 14075DA3140F5DA3141F5DA3143F5DA2147FA214FF01037F001FB612FCA25E42447EC339 >I<003FB500F80103B512E0A326003FF8C8381FF800D91FE0ED07E0013F705A615C96C7 FC60017F16065CA2180E01FF160C91C9FCA2181C4817185BA21838000317305BA2187000 0717605BA218E0120F495EA21701121F495EA21703123F4993C8FCA25F127F491506A217 0E00FF160C90C9FC171CA21718173817304816705F6C5E6C15014C5A4CC9FC6C150E6D14 1E001F5D6D5C6C6CEB01E06C6C495A6C6CEB1F80C6B401FECAFC90387FFFF8011F13E001 0190CBFC43467AC342>I<007FB56C91381FFFF8B65DA2000101E0C8000313006C0180ED 01FCF000F0614E5AA2017F4C5A96C7FC1806A2606E5DA2013F5E1870186060A24D5A6E4A C8FCA2011F1506170E170C5FA26E5C5FA2010F5D16015F4CC9FCA26E13065EA201075C5E A25E16E06E5B4B5A13034BCAFC1506A25D151CECFE185D13015D5DA26E5AA292CBFC5C13 005C5CA25CA25C45467BC339>II<023FB500E0011FB5FCA39126007FFEC7000313 E0DB3FF8913801FE006F486E5A1AF06F6C4A5A626F6C4A5A0706C7FC190E6F6C5C616F6C 5C6171485A6F5D4EC8FC93387FC00660706C5A6060706C5A17F193380FFB8005FFC9FC5F 705AA2707EA3707E5E04067F5E93381C7FC0163816704C6C7EED01C04B486C7E16001506 4B6D7E5D4B6D7E5D5D4A486D7E14034AC76C7E140E5C4A6E7F143002E06F7E495A010370 7E495A131F496C4B7E2603FFE04A487E007F01FC021FEBFFF0B5FCA250447EC351>II<020FB812C05C1A809326800001130003F8C7FCDA3FE04A5A0380 4A5A92C8485A027E4B5A027C4B5A02784B5A4A4B5AA24A4A90C7FC4A4A5A01014B5A4D5A 4A4A5A01034B5A91C8485A4D5AA290C84890C8FC4C5A4C5A4C5A4C5A4C5A4C5A4C5AA24B 90C9FC4B5A4B5A4B5A4B5A4B5A4B5AA24B5A4A90CAFC4A5A4A4814064A5A4A5A4A48140E 4A48140CA24A48141C4990C8121849481538495A49485D495A494815F049485D17014948 14034890C8485A4848150F4848151F48484B5A484815FF48481403043F90C8FC48B8FCB9 FC5F42447BC343>I99 DIII<157E913803FF8091390FC1E0E091391F0073F0027E13334A13 3F4948131F010315E04948130F495AA2494814C0133F4A131F137F91C713805B163F5A49 1500A25E120349147EA216FEA2495CA21501A25EA21503150700015D150F0000141F6D13 3F017CEB77E090383E01E790381F078F903807FE0FD901F85B90C7FC151FA25EA2153FA2 93C7FCA2001C147E007F14FE485C4A5A140348495AEC0FC000F8495A007C01FEC8FC381F FFF8000313C02C407EAB2F>I<14FE137FA3EB01FC13001301A25CA21303A25CA21307A2 5CA2130FA25CA2131FA25CED3FC090393F81FFF0913887C0FC91380E007E023C133ED97F 70133F4A7F4A14805C13FF91C7FC5BA24848143F17005BA200035D167E5BA2000715FE5E 5B1501000F5DA24913035E001F1607030713064914E0150F003FEDC00E170C90C7141CEE 80184816381730007E167017E000FE91380781C0EEC38048913801FF000038EC007C3046 7BC438>I<141E143F5C5CA3147E143891C7FCAE133EEBFF803801C3C0380781E0380601 F0120E121CEA180312381230A2EA700700605BA2EAE00F00C05BEA001F5CA2133F91C7FC A25B137E13FE5BA212015BEC03800003140013F01207495A1406140E140CEBC01C141814 385C00035BEBE1C0C6B45A013EC7FC19437DC121>I<163C16FEA21501A316FCED007016 00AE15FCEC03FF91380F0780021C13C091383803E0147014E014C01301EC800713031400 5B0106130F130E010C14C090C7FC151FA21680A2153FA21600A25DA2157EA215FEA25DA2 1401A25DA21403A25DA21407A25DA2140FA25DA2141F5DA2143F001C91C7FC127F48137E 5CA248485AEB03E038F807C038781F80D83FFEC8FCEA07F0275681C128>I<14FE137FA3 EB01FC13001301A25CA21303A25CA21307A25CA2130FA25CA2131FA25C163F013FECFFC0 923803C0E09138000703ED1E0F491338ED701F017E13E0EC01C001FE018013C00203EB07 004948C8FC140E00015B5C495A5C3803FBC001FFC9FC8014F83807F1FE9038F03F809038 E00FE06E7E000F130381EBC001A2001FED01C017801380A2003F15031700010013F05E48 1506160E007E150C161C00FE01005BED787048EC3FE00038EC0F802B467BC433>II<01F8D903FCEC7F80D803FED91FFF903803FFE0D8 071F903B7C0FC00F81F83E0E0F80E007E01C00FC001C9026C3C0030178137C271807C700 D9F0E0137E02CE902601F1C0133E003801DCDAFB80133F003001D892C7FCD90FF814FF00 70495C0060495CA200E04949485CD8C01F187E4A5C1200040715FE013F6091C75BA2040F 14014960017E5D1903041F5D13FE494B130762043F160E0001060F130C4992C713C0191F 4CED801C00031A1849027E1638F2003004FE167000071A60494A16E0F201C0030192380F 0380000FF18700494AEC03FED80380D90070EC00F84F2D7DAB55>I<01F8EB03FCD803FE EB1FFFD8071F90387C0FC03B0E0F80E007E03A0C07C3C003001CD9C7007F001801CE1301 003801DC80003013D8EB0FF800705B00605BA200E0491303D8C01F5D5C12001607013F5D 91C7FCA2160F495D137E161F5F13FE49143F94C7FC187000014B136049147E16FE4C13E0 000317C049150104F81380170300071700495D170EEE781C000FED7C3849EC1FF0D80380 EC07C0342D7DAB3A>I112 D<91380FC00391383FF0079138F83C0F903903E00E1E 90390FC0063E90381F800790393F00037E4914FC01FE1301485AA2484814F812075B000F 140316F0485AA2003F14074914E0A3007F140F4914C0A3151F90C713805AA2153F6C1500 A2127E5D007F14FE6C1301A214036C6C485A000F131E3807C0383803E0F13901FFC1F838 003F01130014035DA314075DA3140F5DA2141FA2143F011FB51280A21600283F7DAB2B> I<01F8EB0FC0D803FEEB7FF0D8070FEBF038000E903883C07C3A0C07C701FC001C13CE00 18EBDC03003813D8003013F8D90FF013F800709038E000E0006015005C12E0EAC01F5C12 00A2133F91C8FCA35B137EA313FE5BA312015BA312035BA312075BA3120F5BEA0380262D 7DAB2C>I<133ED9FF8014E02603C3C0EB03F0380703E0380601F0000E1507121CD81803 5D12380030150FA2D870075D00605B161FEAE00F00C0495CEA001F4A133FA2013F92C7FC 91C7FC5E5B017E147EA216FE13FE495CA20301EB01801703484802F81300A25F03031306 16F000001407030F130E6D010D130C017C011D131C033913186D9038F0F838903A1F03C0 7870903A07FF803FE0903A01FC000F80312D7DAB38>117 D<013E140ED9FF80EB3F8026 03C3C0137F380703E0380601F0120E121CD81803143F0038151F0030150FA2D870071407 00605BA2D8E00F150000C0497FEA001F4A5B1606133F91C7FC160E49140C137EA2161C01 FE14185B1638163016704848146016E05E150100005D15036D49C7FC1506017C130E017E 5B6D137890380F81E06DB45AD900FEC8FC292D7DAB2F>I<013E1738D9FF80D901C013FC 2603C3C0903907E001FE380703E0380601F0000E150F001C16C0D8180316000038187E00 30031F143E00705ED86007171E5C163FD8E00F92C7121C00C049160CEA001F4A49141C04 7E1418133F91C7FC04FE1438491730017E5CA20301157001FE1760495C19E019C0A24949 481301198018031900606D0107140670130E017C010F5C017E010C1418013ED91CFC1338 6DD9387E13F0903B0FC0F01F01C0903B03FFC00FFF809028007F0001FEC7FC3F2D7DAB46 >I<02FCEB07E0903A03FF801FFC903A0F07C0781E903A1C03E0E01F903A3801F1C07FD9 700013804901FB13FF4848EBFF00495B000316FE90C71438484A130012061401000E5C12 0CC7FC14035DA314075DA3140F5DA3021F143817305D1770023F1460121E003F16E0267F 807FEB01C0026F148000FF01EF1303D901CFEB070000FE903887C00E267C03835B3A3C0F 01E0783A1FFC00FFE0D803F0EB3F80302D7EAB37>I<133ED9FF8014E02603C3C0EB03F0 380703E0380601F0000E1507001C16E0EA180312380030150F007016C0EA60075C161FD8 E00F158000C05BEA001F4A133F1700133F91C7FC5E49147E137EA216FE01FE5C5BA21501 5E485AA215035EA200001407150F6D5C017C131F153F6D13FF90391F03CFC0903807FF8F 903801FC0F90C7121F5EA2153F93C7FCD807C05BD81FE0137E5DA24848485A4A5A01805B 39380007C00018495A001C49C8FC6C137C380781F83803FFE0C66CC9FC2C407DAB30>I< 027CEB018049B413034901801300010F6D5A49EBE00E6F5A90393F03F838903978007EF8 0170EB1FF00160EB01E001E05C49495A90C748C7FC150E5D5D5D5D4A5A4A5A4AC8FC140E 5C5C5C5CEB03C049C9FC130E49141C4914185B49143848481430491470D8039014F048B4 495A3A0FEFC007C0391E03F01FD81C01B55A486C91C7FC485C00606D5A00E0EB3FF048EB 0FC0292D7CAB2D>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fw cmr12 12 83 /Fw 83 128 df<1618163CA2167EA216FFA24B7FA24B6C7EA29238063FE0A24B6C7EA24B 6C7EA292383807FC153092387003FE15609238E001FF15C002016D7F5D02036E7E92C7FC 4A6E7E1406020E6E7E140C021C6E7E141802386E7E143002706E7E146002E06E7E5C0101 6F7F5C0103707E91C9FC183F010683181F4983180F49831807498318034983A249707EA2 4848701380A248CBEA7FC0A20006F03FE0A248F01FF0A2001FBA12F8A24819FCA24819FE A2BCFC48477CC651>1 D<0103B612FCA390C701F0C8FC6F5A6F5AA8913801FFF0023FEB FF80903A01FF3FDFF0D907F0EBC1FCD91FC0EBC07FD93F00EC1F8001FEED0FE048486F7E 48486F7E48486F7E48486F7E001F834982003F1880007F18C0A249163F00FF18E0A8007F 18C06D167FA2003F1880001F18006D5E000F5F6C6C4B5A6C6C4B5A6C6C4B5A6C6C4B5A01 3FED1F80D91FC0027FC7FCD907F0EBC1FCD901FFEBDFF0D9003FB51280020101F0C8FC91 38003FC0A84B7E4B7E0103B612FCA33B447BC346>8 D<027FB67EA39126001FFEC9FC6F 5A6F5AA8B46CEFFF8001E01603D81FF0933807FC006C6C4C5A0007606D161F000360A26D 163F000160AC6C6C5F187FA4D97F804BC7FCA2013F5E02C01401131F02E04A5A010F5ED9 07F01407D903F85DD901FC4A5AD900FE4A5A027F027FC8FCDA1FC713FE0207B512F80201 14C09126001FFCC9FCED07F8A84B7E4B7E027FB67EA341447BC34C>II<9239FFC001FC020F9038F80F FF913B3F803E3F03C0913BFC00077E07E0D903F890390FFC0FF0494890383FF81F4948EB 7FF0495A494814E049C7FCF00FE04991393FC0038049021F90C7FCAFB912F0A3C648C7D8 1FC0C7FCB3B2486CEC3FF0007FD9FC0FB512E0A33C467EC539>I<4AB4FC020F13E09138 7F80F8903901FC001C49487FD907E0130F4948137F011FECFF80495A49C7FCA25B49EC7F 00163E93C7FCACEE3F80B8FCA3C648C7FC167F163FB3B0486CEC7FC0007FD9FC1FB5FCA3 30467EC536>I14 D<00C01430A46C14700060146000 7014E0A26CEB01C0003C13036CEB07806CEB0F00EBE07F3807FFFE000113F86C5BEB1F80 1C1176C431>21 D<121EEA7F8012FF13C0A213E0A3127FEA1E601200A413E013C0A31201 1380120313005A1206120E5A5A5A12600B1D78C41B>39 D<140C141C1438147014E0EB01 C01303EB0780EB0F00A2131E5BA25B13F85B12015B1203A2485AA3485AA348C7FCA35AA2 123EA2127EA4127CA312FCB3A2127CA3127EA4123EA2123FA27EA36C7EA36C7EA36C7EA2 12017F12007F13787FA27F7FA2EB0780EB03C01301EB00E014701438141C140C166476CA 26>I<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378137C133C133E131E131FA2 EB0F80A3EB07C0A3EB03E0A314F0A21301A214F8A41300A314FCB3A214F8A31301A414F0 A21303A214E0A3EB07C0A3EB0F80A3EB1F00A2131E133E133C137C13785BA2485A485AA2 485A48C7FC120E5A5A5A5A5A16647BCA26>I<16C04B7EB3AB007FBAFCBB1280A26C1900 C8D801E0C9FCB3AB6F5A41407BB84C>43 D<121EEA7F8012FF13C0A213E0A3127FEA1E60 1200A413E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B>II<121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A0A78891B>I<14FF010713 E090381F81F890383E007C01FC133F4848EB1F8049130F4848EB07C04848EB03E0A2000F 15F0491301001F15F8A2003F15FCA390C8FC4815FEA54815FFB3A46C15FEA56D1301003F 15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D130F6C6CEB1F806C6CEB3F00 013E137C90381F81F8903807FFE0010090C7FC28447CC131>48 D<143014F01301130313 1F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA3204278C131>II<49B4FC010F13E0013F13FC9038FE01FE3A01F0007F 80D803C0EB3FC048C7EA1FE0120EED0FF0EA0FE0486C14F8A215077F5BA26C48130FEA03 C0C813F0A3ED1FE0A2ED3FC01680ED7F0015FE4A5AEC03F0EC1FC0D90FFFC7FC15F09038 0001FCEC007FED3F80ED1FC0ED0FE016F0ED07F816FC150316FEA2150116FFA3121EEA7F 80487EA416FE491303A2007EC713FC00701407003015F80038140F6C15F06CEC1FE06C6C EB3FC0D803E0EB7F803A01FE01FE0039007FFFF8010F13E0010190C7FC28447CC131>I< ED0380A21507150FA2151F153FA2157F15FFA25CEC03BF153F14071406140C141C141814 301470146014C013011480EB03005B13065B131C13185B1370136013E0485A5B120390C7 FC1206120E120C5A123812305A12E0B812C0A3C8383F8000ADEDFFE0027FEBFFC0A32A43 7DC231>I<000615C0D807C0130701FCEB7F8090B612005D5D5D15E0158026063FFCC7FC 90C9FCAE14FF010713C090381F01F090383800FC01F0137ED807C07F49EB1F8016C090C7 120F000615E0C8EA07F0A316F81503A216FCA5123E127F487EA416F890C712075A006015 F0A20070140F003015E00038EC1FC07E001EEC3F806CEC7F006C6C13FE6C6C485A3901F8 07F039007FFFE0011F90C7FCEB07F826447BC131>I I<121CA2EA1F8090B712C0A3481680A217005E0038C8120C0030151C00705D0060153016 705E5E4814014B5A4BC7FCC81206150E5D151815385D156015E04A5AA24A5A140792C8FC 5CA25C141E143EA2147E147CA214FCA21301A3495AA41307A6130FAA6D5AEB01C02A457B C231>I<14FF010713E0011F13F890387F00FE01FC133FD801F0EB1F804848EB0FC049EB 07E00007EC03F048481301A290C713F8481400A47FA26D130116F07F6C6CEB03E013FC6C 6CEB07C09039FF800F806C9038C01F006CEBF03EECF87839007FFEF090383FFFC07F0107 7F6D13F8497F90381E7FFFD97C1F1380496C13C02601E00313E048486C13F00007903800 7FF84848EB3FFC48C7120F003EEC07FE150148140016FF167F48153FA2161FA56C151E00 7C153EA2007E153C003E157C6C15F86DEB01F06C6CEB03E06C6CEB07C0D803F8EB1F80C6 B4EBFF0090383FFFFC010F13F00101138028447CC131>I<14FF010713E0011F13F89038 7F80FC9038FC007E48487F4848EB1F804848EB0FC0000FEC07E0485AED03F0485A16F800 7F140190C713FCA25AA216FE1500A516FFA46C5CA36C7E5D121F7F000F5C6C6C1306150E 6C6C5B6C6C5BD8007C5B90383F01E090390FFF80FE903801FE0090C8FC150116FCA4ED03 F8A216F0D80F801307486C14E0486C130F16C0ED1F80A249EB3F0049137E001EC75A001C 495A000F495A3907E01FE06CB51280C649C7FCEB1FF028447CC131>I<121EEA7F80A2EA FFC0A4EA7F80A2EA1E00C7FCB3A5121EEA7F80A2EAFFC0A4EA7F80A2EA1E000A2B78AA1B >I<121EEA7F80A2EAFFC0A4EA7F80A2EA1E00C7FCB3A5121E127FEAFF80A213C0A4127F 121E1200A512011380A3120313005A1206120E120C121C5A5A12600A3E78AA1B>I<007F BAFCBB1280A26C1900CEFCB0007FBAFCBB1280A26C190041187BA44C>61 D<16C04B7EA34B7EA34B7EA34B7EA3ED19FEA3ED30FFA203707FED607FA203E07FEDC03F A2020180ED801FA2DA03007F160FA20206801607A24A6D7EA34A6D7EA34A6D7EA2027081 0260147FA202E08191B7FCA249820280C7121FA249C87F170FA20106821707A2496F7EA3 496F7EA3496F7EA201788313F8486C83D80FFF03037FB500E0027FEBFFC0A342477DC649 >65 DI< DB0FFE146092B500C013E0020314F0913A0FFC01FC0191393FC0003E02FFC7EA0F83D903 FCEC03C74948EC01E74948EC00FF4948157F4948153F4948151F49C9120F485A49160712 0348481603A248481601A248481600A2123FA2491760127FA31900485AAE6C7EA21960A2 123F7FA2001F18E07F000F18C0A26C6C160119806C6C160312016DEE07006C6C16066D6C 150E6D6C5D6D6C5D6D6C15786D6C5D6D6C4A5AD900FFEC0780DA3FC0011FC7FCDA0FFC13 FC0203B512F0020014C0DB0FFEC8FC3B487BC546>II< B912F8A3000101C0C7127F6C6C48EC07FC17011700187C183C181CA284A31806A4180704 067FA395C7FCA4160EA2161E163E16FE91B5FCA3EC8000163E161E160EA21606A319C0A3 F0018093C7FCA41803A21900A260A260A2181EA2183E187EEF01FE170748486C147FB95A A33A447CC342>IIIII< 010FB512FEA3D9000313806E130080B3B3AB123F487E487EA44A5A13801300006C495A00 705C6C13076C5C6C495A6CEB1F802603E07FC7FC3800FFFCEB1FE027467BC332>IIIIIII82 D<49B41303010FEBE007013F13F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48 486DB4FC48C8FC4881003E81127E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA 3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15C0013F14F0010F80010180D900 1F7F14019138001FFF03031380816F13C0167F163F161F17E000C0150FA31607A37EA36C 16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC0 0FE0D8E00FB51280010149C7FC39C0003FF02B487BC536>I<003FB912F8A3903BF0001F F8001F01806D481303003EC7150048187C0078183CA20070181CA30060180CA5481806A5 C81600B3B3A54B7EED7FFE49B77EA33F447DC346>IIII89 D<001FB81280A3912680000113 0001FCC7FC01F04A5A01C04A5A5B90C8485A121E4C5A484B5AA200384B5A4C5AA24B90C7 FC00304A5AA24B5AA24B5AC8485AA24B5A4B5AA24B5A5C93C8FC4A5AA24A5A4A5AA24A5A 4A5AA24A5A14FF5D4990C9FCEF0180495A495AA2495A494814031800495AA2495A495A5F 4890C8FC485A5F485A48485D5F48485D17FE484814034848140F16FFB8FCA331447BC33C >II93 D97 DII<167FED3FFFA315018182B3EC7F80 903803FFF090380FC07C90383F000E017E1307496D5AD803F87F48487F5B000F81485AA2 485AA2127FA290C8FC5AAB7E7FA2123FA26C7EA2000F5D7F6C6C5B00035C6C6C9038077F 806C6C010E13C0013F011C13FE90380FC0F8903803FFE09026007F0013002F467DC436> IIIIII<143C14FFA2491380A46D1300A2 143C91C7FCADEC7F80EB3FFFA31300147F143FB3B3AA123E127F39FF807F00A2147EA25C 6C485A383C01F06C485A3807FF80D801FEC7FC195785C21E>IIII<3901FC01FE00FF903807FFC091381E07 F091383801F8000701707F0003EBE0002601FDC07F5C01FF147F91C7FCA25BA35BB3A848 6CECFF80B5D8F83F13FEA32F2C7DAB36>I I<3901FC03FC00FF90380FFF8091383C07E091387001F83A07FDE000FE00010180137F01 FFEC3F8091C7EA1FC04915E049140F17F0160717F8160317FCA3EE01FEABEE03FCA3EE07 F8A217F0160F6D15E0EE1FC06D143F17806EEB7E00D9FDC05B9039FCF003F891383C0FE0 91381FFF80DA03FCC7FC91C9FCAE487EB512F8A32F3F7DAB36>I<91387F8003903903FF E00790380FE07890393F801C0F90387E000E496D5AD803F8EB039F0007EC01BF4914FF48 487F121F5B003F81A2485AA348C8FCAB6C7EA3123F7F121F6D5C120F6D5B12076C6C5B6C 6C497E6C6C130E013F131C90380FC0F8903803FFE09038007F0091C7FCAEEEFF80033F13 FEA32F3F7DAB33>I<3903F803F000FFEB1FFCEC3C3EEC707F0007EBE0FF3803F9C00001 5B13FBEC007E153C01FF13005BA45BB3A748B4FCB512FEA3202C7DAB26>I<90383FE018 3901FFFC383907E01F78390F0003F8001E1301481300007C1478127800F81438A21518A2 7EA27E6C6C13006C7E13FC383FFFE06C13FC6C13FF6C14C06C14E0C614F0011F13F81300 EC0FFC140300C0EB01FE1400157E7E153EA27EA36C143C6C147C15786C14F86CEB01F039 F38003E039F1F00F8039E07FFE0038C00FF01F2E7DAC26>I<1306A5130EA4131EA3133E 137EA213FE12011207001FB512F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D 133890381F8030ECC070903807E0E0903801FFC09038007F001E3E7EBC26>IIIIII<003FB612E0A29038C0003F90C713 C0003CEC7F800038ECFF00A20030495A0070495AA24A5A0060495AA24A5A4A5AA2C7485A 4AC7FC5B5C495A13075C495A131F4A1360495A495AA249C712C0485AA2485A485A150148 5A48481303A24848EB07804848131F00FF14FF90B6FCA2232B7DAA2B>I124 D<01F81302D803FE13073907FF800E48EBE01C391F1FF8F8393807FFF0D8 700113E039E0007FC00040EB1F00200978C131>126 D<001EEB0780007FEB0FE039FF80 1FF0EBC03FA4EB801F397F000FE0001EEB07801C0A76C231>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fx cmbx12 12 49 /Fx 49 125 df12 D39 D45 DI< EC3FF849B5FC010F14E0013F14F890397FF01FFC9039FFC007FE4890380001FF48486D13 80000716C049147F000F16E049143F001F16F0A2003F16F8A249141F007F16FCA600FF16 FEB3A3007F16FCA56C6CEC3FF8A3001F16F0A2000F16E06D147F000716C06D14FF6C6C49 13806C6D4813006C6D485A90397FF01FFC6DB55A010F14E0010314809026003FF8C7FC2F 427CC038>48 DIII<163FA25E5E5D 5DA25D5D5D5DA25D92B5FCEC01F7EC03E7140715C7EC0F87EC1F07143E147E147C14F8EB 01F0EB03E0130714C0EB0F80EB1F00133E5BA25B485A485A485A120F5B48C7FC123E5A12 FCB91280A5C8000F90C7FCAC027FB61280A531417DC038>I<0007150301E0143F01FFEB 07FF91B6FC5E5E5E5E5E16804BC7FC5D15E092C8FC01C0C9FCAAEC3FF001C1B5FC01C714 C001DF14F09039FFE03FFC9138000FFE01FC6D7E01F06D13804915C0497F6C4815E0C8FC 6F13F0A317F8A4EA0F80EA3FE0487E12FF7FA317F05B5D6C4815E05B007EC74813C0123E 003F4A1380D81FC0491300D80FF0495AD807FEEBFFFC6CB612F0C65D013F1480010F01FC C7FC010113C02D427BC038>I<4AB47E021F13F0027F13FC49B6FC01079038807F809039 0FFC001FD93FF014C04948137F4948EBFFE048495A5A1400485A120FA248486D13C0EE7F 80EE1E00003F92C7FCA25B127FA2EC07FC91381FFF8000FF017F13E091B512F89039F9F0 1FFC9039FBC007FE9039FF8003FF17804A6C13C05B6F13E0A24915F0A317F85BA4127FA5 123FA217F07F121FA2000F4A13E0A26C6C15C06D4913806C018014006C6D485A6C9038E0 1FFC6DB55A011F5C010714C0010191C7FC9038003FF02D427BC038>I<121E121F13FC90 B712FEA45A17FC17F817F017E017C0A2481680007EC8EA3F00007C157E5E00785D15014B 5A00F84A5A484A5A5E151FC848C7FC157E5DA24A5A14035D14074A5AA2141F5D143FA214 7F5D14FFA25BA35B92C8FCA35BA55BAA6D5A6D5A6D5A2F447AC238>III65 DII70 DI73 D75 DI78 D82 DI<003F BA12E0A59026FE000FEB8003D87FE09338003FF049171F90C71607A2007E1803007C1801 A300781800A400F819F8481978A5C81700B3B3A20107B8FCA545437CC24E>I89 D<903801FFE0011F13FE017F6D7E48B612E03A03FE007FF848 48EB1FFC6D6D7E486C6D7EA26F7FA36F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC13 07013F13F19038FFFC01000313E0000F1380381FFE00485A5B127F5B12FF5BA35DA26D5B 6C6C5B4B13F0D83FFE013EEBFFC03A1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90F FCC9FC322F7DAD36>97 DIIII< EDFF80020F13E0027F13F049B512F849EB8FFC90390FFE0FFE90381FFC1F14F8133FEB7F F0A2ED0FFCEBFFE0ED03F0ED00C01600ABB612F8A5C601E0C7FCB3B0007FEBFFE0A52746 7DC522>III<137C48B4FC4813804813C0A24813E0A56C13C0A26C13806C1300EA007C 90C7FCAAEB7FC0EA7FFFA512037EB3AFB6FCA518467CC520>I108 D<90277F8007FEEC0FFCB590263FFFC090387FFF80 92B5D8F001B512E002816E4880913D87F01FFC0FE03FF8913D8FC00FFE1F801FFC0003D9 9F009026FF3E007F6C019E6D013C130F02BC5D02F86D496D7EA24A5D4A5DA34A5DB3A7B6 0081B60003B512FEA5572D7CAC5E>I<90397F8007FEB590383FFF8092B512E0028114F8 913987F03FFC91388F801F000390399F000FFE6C139E14BC02F86D7E5CA25CA35CB3A7B6 0083B512FEA5372D7CAC3E>II<90397FC00FF8B590B57E02C314E002CF14F89139DFC03FFC9139FF001FFE000301FC EB07FF6C496D13804A15C04A6D13E05C7013F0A2EF7FF8A4EF3FFCACEF7FF8A318F017FF A24C13E06E15C06E5B6E4913806E4913006E495A9139DFC07FFC02CFB512F002C314C002 C091C7FCED1FF092C9FCADB67EA536407DAC3E>I<90387F807FB53881FFE0028313F002 8F13F8ED8FFC91389F1FFE000313BE6C13BC14F8A214F0ED0FFC9138E007F8ED01E092C7 FCA35CB3A5B612E0A5272D7DAC2E>114 D<90391FFC038090B51287000314FF120F381F F003383FC00049133F48C7121F127E00FE140FA215077EA27F01E090C7FC13FE387FFFF0 14FF6C14C015F06C14FC6C800003806C15806C7E010F14C0EB003F020313E0140000F014 3FA26C141F150FA27EA26C15C06C141FA26DEB3F8001E0EB7F009038F803FE90B55A00FC 5CD8F03F13E026E007FEC7FC232F7CAD2C>IIIII<001FB71280A49026FC001F130001E0495A 5B49495A90C7485A48495B123E4A5B4A5B003C495BA24A90C7FC4A5A4A5AC7FC4A5A495B 495BA2495B499038800780491300A2495A4948130F49481400A2485B48495B485BA24849 5B4890C75A48485C15034848EB1FFEB7FCA4292C7DAB32>122 D 124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fy cmr7 7 1 /Fy 1 50 df<13381378EA01F8121F12FE12E01200B3AB487EB512F8A215267BA521>49 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: Fz cmex10 10 2 /Fz 2 2 df<1430147014E0EB01C01303EB0780EB0F00A2131E5BA25B13F85B12015B12 03A2485AA3485AA3121F90C7FCA25AA3123EA2127EA6127C12FCB3A2127C127EA6123EA2 123FA37EA27F120FA36C7EA36C7EA212017F12007F13787FA27F7FA2EB0780EB03C01301 EB00E0147014301462738226>0 D<12C07E12707E123C7E7EA26C7E6C7EA26C7E7F1200 7F1378137CA27FA37FA31480130FA214C0A31307A214E0A6130314F0B3A214E01307A614 C0A2130FA31480A2131F1400A3133EA35BA2137813F85B12015B485AA2485A48C7FCA212 1E5A12385A5A5A14627C8226>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FA msbm10 10 2 /FA 2 81 df67 D<007FB612C0B712FC6C15FF2703C01E071380000190393C01 C7E00238EBE1F0923800E0F81738EEF03CEE701C171E170EA7171E171CEEF03CEEE03817 F8923801E1F0EEC7E0923803FF80023FB5120016FC16E00238C8FCB3A60003133C007FB5 12F0B6FC7E2F397EB834>80 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FB cmmi7 7 3 /FB 3 114 df<1238127C12FE12FFA2127F123B1203A31206A3120C1218123812701220 08127A8614>59 D<9038F007C03901FC1FF039031E78780006EBE03C90381FC01C000CEB 801E14005B0018141F133E1200137E153E137CA213FC157C5B1578000114F0A2EC01E0EC 03C03903FC07809038FE1F00EBE7FCEBE1F0D807E0C7FCA25BA2120FA25B121FEAFFF8A2 2025809922>112 DI E %EndDVIPSBitmapFont %DVIPSBitmapFont: FC cmmi10 10 4 /FC 4 114 df<150C151E153EA2153C157CA2157815F8A215F01401A215E01403A215C0 1407A21580140FA215005CA2141E143EA2143C147CA2147814F8A25C1301A25C1303A249 5AA25C130FA291C7FC5BA2131E133EA2133C137CA2137813F8A25B1201A25B1203A25B12 07A25B120FA290C8FC5AA2121E123EA2123C127CA2127812F8A25A12601F537BBD2A>61 D71 D<90390F8003F090391FE00FFC903939F03C1F 903A70F8700F80903AE0FDE007C09038C0FF80030013E00001491303018015F05CEA0381 13015CA2D800031407A25CA20107140FA24A14E0A2010F141F17C05CEE3F80131FEE7F00 4A137E16FE013F5C6E485A4B5A6E485A90397F700F80DA383FC7FC90387E1FFCEC07E001 FEC9FCA25BA21201A25BA21203A25B1207B512C0A32C3583A42A>112 D<02FC13C0903803FF0190380F838390383F01C790397E00EF8049137F485A4848133F00 0715005B485A001F5C157E485AA2007F14FE90C75AA3481301485CA31403485CA314075D 140F127C141F007E495A003E137F381F01EF380F839F3903FF1F80EA00FC1300143F92C7 FCA35C147EA314FE5C130190387FFFF0A322357DA425>I E %EndDVIPSBitmapFont %DVIPSBitmapFont: FD cmr10 10 53 /FD 53 128 df12 D<127812FCA27E7EEA7F80121FEA0FC0EA07E0EA 03F012001378133C131E13060F0F77B92A>18 D<133C137EA213FE1201EA03FC13F0EA07 E0EA0FC0EA1F80EA1E005A5A5A12C00F0F6FB92A>I<121C127FEAFF80A213C0A3127F12 1C1200A412011380A2120313005A1206120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E131E5B5BA25B485AA2485AA212075B120F90C7FC A25A121EA2123EA35AA65AB2127CA67EA3121EA2121F7EA27F12077F1203A26C7EA26C7E 1378A27F7F130E7FEB0380EB01C0EB00E01460135278BD20>I<12C07E12707E7E7E120F 6C7E6C7EA26C7E6C7EA21378A2137C133C133E131EA2131F7FA21480A3EB07C0A6EB03E0 B2EB07C0A6EB0F80A31400A25B131EA2133E133C137C1378A25BA2485A485AA2485A48C7 FC120E5A5A5A5A5A13527CBD20>I<15301578B3A6007FB812F8B912FCA26C17F8C80078 C8FCB3A6153036367BAF41>43 D<121C127FEAFF80A213C0A3127F121C1200A412011380 A2120313005A1206120E5A5A5A12600A19798817>II<121C127F EAFF80A5EA7F00121C0909798817>I48 DIII<0006140CD80780133C9038F003F890B5FC5D5D158092C7FC14FC 38067FE090C9FCABEB07F8EB3FFE9038780F803907E007E090388003F0496C7E12066E7E C87EA28181A21680A4123E127F487EA490C71300485C12E000605C12700030495A00385C 6C1303001E495A6C6C485A3907E03F800001B5C7FC38007FFCEB1FE0213A7CB72A>53 D<913A01FF800180020FEBE003027F13F8903A01FF807E07903A03FC000F0FD90FF0EB03 9F4948EB01DFD93F80EB00FF49C8127F01FE153F12014848151F4848150FA248481507A2 485A1703123F5B007F1601A35B00FF93C7FCAD127F6DED0180A3123F7F001F160318006C 7E5F6C7E17066C6C150E6C6C5D00001618017F15386D6C5CD91FE05C6D6CEB03C0D903FC EB0F80902701FF803FC7FC9039007FFFFC020F13F002011380313D7BBA3C>67 D69 D71 D75 DII79 DI83 D<003FB812E0A3D9C003EB 001F273E0001FE130348EE01F00078160000701770A300601730A400E01738481718A4C7 1600B3B0913807FF80011FB612E0A335397DB83C>II87 D97 DIIII<147E903803FF8090380FC1E0EB1F8790 383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8 A31C3B7FBA19>IIII< EB01C0EB07F0EB0FF8A5EB07F0EB01C090C7FCAAEB01F813FFA313071301B3B3A2123C12 7E00FF13F01303A214E038FE07C0127C383C0F00EA0FFEEA03F8154984B719>I108 D<2703F00FF0EB1FE000FFD9 3FFCEB7FF8913AF03F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013CE01 FE14DC49D907F8EB0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA34025 7EA445>I<3903F00FF000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F70013FE 496D7EA25BA35BB3A3486C497EB500C1B51280A329257EA42E>II<39 03F01FE000FFEB7FF89038F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB03F0 4914F849130116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB0FE0 01F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328357E A42E>II<3807E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE9038 EC03E09038FC0080491300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313F812 0112031207001FB5FCB6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E13006D5A EB0FFEEB01F81A347FB220>IIIII< B538803FFEA33A0FF8000FF06C48EB07C00003EC03806C7E16007F00001406A2017E5BA2 137F6D5BA26D6C5AA2ECC070010F1360A26D6C5AA214F101035BA2D901FBC7FCA214FF6D 5AA2147CA31438A21430A214701460A25CA2EA7C0100FE5B130391C8FC1306EAFC0EEA70 1C6C5AEA1FF0EA0FC027357EA32C>I124 D<001C131C007F137F39FF80FF80A5397F007F00001C131C190978B72A>127 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FE cmcsc10 10 21 /FE 21 125 df<133C137EA213FE1201EA03FC13F0EA07E0EA0FC0EA1F80EA1E005A5A5A 12C00F0F6DB92E>19 D<121C127FEAFF80A5EA7F00121C090977881B>46 D<150EA3151FA24B7EA34B7EA3EDDFE0A202017F158FA29138030FF81507A202067F1503 020E7FEC0C01A2021C7FEC1800A24A80167FA24A6D7EA202E0804A131FA2494880160FA2 49B67EA249810106C71203A249811601A2498182A2496F7EA20170820160153F13E06D82 1203D80FFCED7FF8B56C010FB512E0A33B3C7CBB44>65 D71 D<011FB512F0A39039000FFE00EC03FCB3B3A3123FEA7F80EAFFC0A44A5A1380D87F005B 0070130F6C495A6C5C6C49C7FC3807C0FE3801FFF838003FC0243B7CB82F>74 D82 D<1407A24A7EA34A7EA3EC37E0A2EC 77F01463A2ECC1F8A201017F1480A2903803007EA301067FA2010E80010C131FA2496D7E A2013FB57EA29038300007496D7EA3496D7EA200018149130012036D801207D81FE09038 01FF80D8FFF8010F13F8A22D2C7DAB33>97 DI<91383FC006903901FFF80E90390FE03E1E90 381F0007017EEB03BE01F8EB01FE484813004848147E0007153E485A001F151E5B003F15 0E90C8FC5A1606A212FE1600AA007F1506A37E6D140E001F150C7F000F151C6C6C141800 0315386C6C14706C6C14E0017EEB01C0011FEB078090390FE03E00903801FFF89038003F C0272D7BAB31>I101 D105 D108 DII114 D<017F13603901FFE0E0380780F9380E001F48130748 130312780070130100F01300A315607EA26C14007E127F13C0EA3FFEEBFFE06C13F80007 13FE6C7FC61480010F13C01300EC0FE01407EC03F01401A212C01400A37E15E06C1301A2 6CEB03C06CEB0780B4EB0F0038F3E01E38E0FFF838C01FE01C2D7BAB26>I<007FB712C0 A23A7E003FC00F007890381F8003007015011600126000E016E0A2481660A5C71500B3A8 EC7FE0011FB57EA22B2B7DAA31>III<3B7FFF800FFFC0A2000790390003FE00 6C48EB01F800015D000015C0017F13036D5C6E48C7FC90381FC0066D6C5A151C6D6C5A90 3803F83001015BECFCE06D6C5AEC7F80A2143F6E7E140F4A7E4A7E1433EC63F8ECE1FCEC C0FE903801807E0103137F49486C7E0106131F4980011C6D7E496D7E0130130301708001 F06D7E000181000781D81FF8491380B46C4913F8A22D2B7DAA33>120 D124 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FF cmr12 14.4 11 /FF 11 121 df71 D<49B612FEA490C7003F138092380FFE 001507B3B3B3A21206EA3FC0487E487EA44B5AA25B007F5D0180131F0078C75B6C143F00 3E4A5A6C5D6C6C495A2707E003FEC7FC3901FC07FC6CB512F0013F13C0D907FCC8FC2F54 7BD13C>74 D97 D101 D<1378EA01FE487E487FA66C90C7FC6C5AEA00 7890C8FCB0EB7F80B5FCA41203C6FC137FB3B3A43801FFE0B61280A419507CCF21>105 D108 D<01FFEB07FCB590383FFF8092B512E0913901F00FF8913903C007FC000349C66C7EC601 0E13016D486D7E5C143002706E7E146014E05CA35CB3AD2601FFE0903801FFE0B600C0B6 12C0A43A347CB341>110 D<01FFEB1F80B5EB7FF0913801FFF8913803E1FC91380783FE 0003EB0F07C6131EEB7F1C1438143091387003FC91386000F0160014E05CA45CB3AA8048 487EB612F0A427347DB32E>114 D117 DI<007FB5D8800FB51280A4 C69026FC0003EBF000D93FF86D1380011F4BC7FC010F15F801075D6D6C5C6E495A6D6C5C 6D14076E6C48C8FCEDC01E6E6C5A021F133891380FF0786F5A913807FDE002035BEC01FF 5E80157F6F7E824B7E15FFEDE7F802017F913803C3FEEC07814AC67E020E80021E6D7E4A 133F4A6D7E4A80707E4948130749486D7E010781010F6E7E013F8201FF8200076D010713 F0B500F8011FEBFFE0A43B337FB23E>120 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FG cmti12 14.4 2 /FG 2 122 df98 D121 D E %EndDVIPSBitmapFont %DVIPSBitmapFont: FH cmbx12 14.4 16 /FH 16 87 df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ndDVIPSBitmapFont end %%EndProlog %%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: a4 %%EndSetup %%Page: 1 1 1 0 bop 35 523 3780 4 v 92 989 a FH(TIAN'S)57 b(INV)-15 b(ARIANT)58 b(OF)g(THE)g(GRASSMANN)f(MANIF)l(OLD)1451 1315 y FG(by)81 b FF(Julien)38 b(Griv)-7 b(aux)p 1358 1642 1134 4 v 390 2223 a FE(Abstra)n(ct.)40 b(|)28 b FD(W)-7 b(e)28 b(pro)n(v)n(e)e(that)h(Tian's)h(in)n(v)-5 b(arian)n(t)26 b(on)h(the)h(complex)f(Grassmann)g(manifold)390 2309 y FC(G)455 2321 y FB(p;q)546 2309 y FD(\()p FA(C)i FD(\))46 b(is)39 b(equal)h(to)f(1)p FC(=)p FD(\()p FC(p)26 b FD(+)g FC(q)s FD(\).)74 b(The)40 b(metho)r(d)g(in)n(tro)r(duced)f (here)h(uses)f(a)g(Lie)h(group)f(of)390 2399 y(holomorphic)29 b(isometries)h(whic)n(h)g(op)r(erates)g(transitiv)n(ely)f(on)i(the)g (considered)e(manifolds)i(and)390 2498 y(a)c(natural)g(im)n(b)r(edding) h(of)1250 2431 y Fz(\000)1288 2498 y FA(P)1340 2468 y Fy(1)1376 2498 y FD(\()p FA(C)h FD(\))1509 2431 y Fz(\001)1553 2448 y FB(p)1619 2498 y FD(in)f FC(G)1781 2510 y FB(p;q)1871 2498 y FD(\()p FA(C)i FD(\).)390 2739 y FE(R)456 2732 y(\023)456 2739 y(esum)653 2732 y(\023)653 2739 y(e.)37 b(|)32 b FD(On)g(prouv)n(e)g(que)g(l'in)n(v)-5 b(arian)n(t)31 b(de)i(Tian)f(sur)g(la)g(grassmannienne)f FC(G)3097 2751 y FB(p;q)3188 2739 y FD(\()p FA(C)e FD(\))39 b(est)390 2833 y(1)p FC(=)p FD(\()p FC(p)13 b FD(+)g FC(q)s FD(\).)26 b(La)f(m)n(\023)-39 b(etho)r(de)25 b(pr)n(\023)-39 b(esen)n(t)n(\023)g (ee)23 b(dans)i(cet)g(article)g(utilise)h(un)f(group)r(e)g(de)g(Lie)h (d'isom)n(\023)-39 b(etries)390 2920 y(holomorphes)25 b(qui)h(op)n(\022)-39 b(ere)25 b(transitiv)n(emen)n(t)h(sur)g(les)g(v) -5 b(ari)n(\023)-39 b(et)n(\023)g(es)24 b(consid)n(\023)-39 b(er)n(\023)g(ees)23 b(ainsi)j(qu'un)h(plonge-)390 3019 y(men)n(t)h(naturel)f(de)997 2952 y Fz(\000)1035 3019 y FA(P)1087 2989 y Fy(1)1123 3019 y FD(\()p FA(C)i FD(\))1255 2952 y Fz(\001)1299 2969 y FB(p)1365 3019 y FD(dans)e FC(G)1624 3031 y FB(p;q)1715 3019 y FD(\()p FA(C)i FD(\).)1545 3320 y Fx(1.)56 b(In)m(tro)s(duction)35 3518 y Fw(On)27 b(a)f(complex)g(manifold,)f(an)i(hermitian)d(metric)h Fv(h)i Fw(is)f(c)m(haracterized)h(b)m(y)h(the)f Fu(1-1)i(symple)-5 b(ctic)31 b Fw(form)35 3658 y Fv(!)36 b Fw(de\014ned)e(b)m(y)g Fv(!)d Fw(=)c Fv(i)17 b(g)896 3673 y Ft(\025)p 949 3635 31 3 v -1 x(\026)1000 3658 y Fv(dz)1100 3621 y Ft(\025)1168 3658 y Fs(^)23 b Fv(d)p 1325 3603 34 4 v(z)1357 3621 y Ft(\026)1404 3658 y Fw(,)32 b(where)i Fv(g)1792 3673 y Ft(\025)p 1845 3635 31 3 v -1 x(\026)1907 3658 y Fw(=)28 b Fv(h)2067 3673 y Ft(\025)p 2120 3635 V -1 x(\026)2155 3658 y Fv(=)p Fw(2.)35 3797 y(The)34 b(metric)d(is)i(a)f Fu(K\177)-50 b(ahler)34 b(metric)k Fw(if)31 b Fv(!)36 b Fw(is)c(closed,)h(i.)43 b(e.)h Fv(d!)30 b Fw(=)e(0;)k(then)h Fv(M)44 b Fw(is)32 b(a)g Fu(K\177)-50 b(ahler)34 b(manifold)p Fw(.)35 3936 y(On)47 b(a)f(K\177)-49 b(ahler)46 b(manifold,)i(w)m(e)f (can)g(de\014ne)h(the)f Fu(R)n(ic)-5 b(ci)47 b(form)54 b Fw(b)m(y)47 b Fv(R)53 b Fw(=)e Fv(i)17 b(R)2961 3951 y Ft(\025)p 3014 3914 V(\026)3066 3936 y Fv(dz)3166 3900 y Ft(\025)3243 3936 y Fs(^)32 b Fv(d)p 3409 3882 34 4 v(z)3442 3900 y Ft(\026)3488 3936 y Fw(,)51 b(where)35 4076 y Fv(R)109 4091 y Ft(\025)p 163 4053 31 3 v 1 w(\026)225 4076 y Fw(=)28 b Fs(\000)p Fv(@)457 4091 y Ft(\025)p 511 4053 V 1 w(\026)562 4076 y Fw(log)17 b Fs(j)p Fv(g)t Fs(j)p Fw(.)35 4215 y(A)40 b(K\177)-49 b(ahler)39 b(manifold)f(is)h Fu(Einstein)i(with)h(factor)f Fv(k)i Fw(if)c Fv(R)i Fw(=)f Fv(k)s(!)t Fw(.)65 b(F)-8 b(or)39 b(instance,)j(c)m(ho)s(osing)e(a)f (lo)s(cal)35 4355 y(co)s(ordinate)e(system)i Fv(Z)44 b Fw(=)37 b(\()p Fv(z)1156 4370 y Fr(1)1195 4355 y Fv(;)17 b(:)g(:)g(:)f(;)h(z)1459 4370 y Ft(m)1526 4355 y Fw(\),)39 b(the)f(pro)5 b(jectiv)m(e)39 b(space)g Fq(P)2586 4370 y Ft(m)2655 4355 y Fw(\()p Fq(C)e Fw(\))43 b(with)38 b(the)g(F)-8 b(ubini-Study)35 4494 y(metric)32 b Fv(!)f Fw(=)c Fv(i@)p 641 4413 41 4 v 6 w(@)c Fw(log)824 4414 y Fp(\000)870 4494 y Fw(1)f(+)g Fs(jj)p Fv(Z)7 b Fs(jj)1225 4458 y Fr(2)1263 4414 y Fp(\001)1341 4494 y Fw(is)32 b(Einstein)g(with)h(factor)f Fv(m)22 b Fw(+)g(1.)35 4634 y(On)42 b(a)f(K\177)-49 b(ahler)41 b(manifold)e Fv(M)10 b Fw(,)45 b(the)d Fu(\014rst)h(Chern)g(class)49 b Fv(C)2233 4598 y Fr(1)2272 4634 y Fw(\()p Fv(M)10 b Fw(\))42 b(is)g(the)g (cohomology)e(class)h(of)g(the)35 4773 y(Ricci)f(tensor,)k(that)d(is)g (the)g(set)h(of)f(the)g(forms)g Fv(R)29 b Fw(+)f Fv(i@)p 2171 4692 V 5 w(@)7 b(')p Fw(,)43 b(where)f Fv(')f Fw(is)g Fv(C)2925 4737 y Fo(1)3041 4773 y Fw(on)g Fv(M)10 b Fw(.)69 b(If)42 b(there)f(is)p 35 4892 499 4 v 35 4975 a Fn(11th)31 b(De)l(c)l(emb)l(er)f(2005)118 5100 y Fm(\017)83 b Fn(E-mail)31 b(:)d Fl(julien.grivaux@f)o(re)o(e.f)o(r)37 b FE(Julien)32 b(Griv)-7 b(a)n(ux)p FD(,)27 b(Univ)n(ersit)n(\023)-39 b(e)26 b(Pierre)g(et)i(Marie)e(Curie)35 5224 y(2000)g(Mathematics)h (Sub)5 b(ject)29 b(Classi\014cation.)34 b(|)41 b(53C55,)26 b(32M10.)35 5339 y(Key)j(w)n(ords)e(and)i(phrases.)34 b(|)42 b(K\177)-42 b(ahler)27 b(manifold,)j(Einstein-K\177)-42 b(ahler)27 b(metric,)i(\014rst)g(Chern)f(class,)g(admissible)h(func-)35 5459 y(tions,)f(Tian's)f(in)n(v)-5 b(arian)n(t,)27 b(grassmannian.)p eop %%Page: 2 2 2 1 bop 35 283 a Fk(2)1490 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 619 y Fw(a)37 b(form)f(in)h Fv(C)552 583 y Fr(1)591 619 y Fw(\()p Fv(M)10 b Fw(\))38 b(whic)m(h)g(is)e(p)s(ositiv)m(e)h (\(resp.)58 b(negativ)m(e,)39 b(zero\),)f(then)g Fv(C)2855 583 y Fr(1)2895 619 y Fw(\()p Fv(M)10 b Fw(\))37 b(is)g Fu(p)-5 b(ositive)44 b Fw(\(resp.)35 759 y Fu(ne)-5 b(gative)p Fw(,)43 b Fu(zer)-5 b(o)6 b Fw(\).)67 b(If)41 b(a)g(K\177)-49 b(ahler)39 b(manifold)f(is)j(Einstein,)h(then)g Fv(C)2524 723 y Fr(1)2563 759 y Fw(\()p Fv(M)10 b Fw(\))41 b(and)g Fv(k)j Fw(are)d(b)s(oth)g(p)s(ositiv)m(e)35 898 y(\(resp.)75 b(negativ)m(e,)45 b(zero\).)74 b(In)43 b(the)g(negativ)m(e)f(case,)k (it)c(w)m(as)h(pro)m(v)m(ed)h(b)m(y)g(Aubin)e(\([)p Fx(Au1)p Fw(],)j(see)f(also)35 1038 y([)p Fx(Au4)p Fw(]\),)37 b(that)e(there)h(exists)g(a)f(unique)h(Einstein-K\177)-49 b(ahler)34 b(metric)h(\(E.K.)g(metric\))g(on)g Fv(M)46 b Fw(.)52 b(It)36 b(is)f(so)35 1177 y(for)c(the)h(zero)g(case)h(to)s(o) e(\([)p Fx(Au1)p Fw(],)h([)p Fx(Y)-9 b(a)o Fw(]\).)44 b(The)32 b(question)g(for)f(the)h(p)s(ositiv)m(e)f(case)i(is)e(still)e (op)s(en:)43 b(some)35 1317 y(manifolds,)g(suc)m(h)h(as)f(the)g (complex)f(pro)5 b(jectiv)m(e)43 b(space)h(blo)m(wn)e(up)h(at)f(one)h (p)s(oin)m(t,)h(do)e(not)h(admit)35 1456 y(an)e(E.K.)g(metric)e(\(for)h (obstructions,)j(see)f([)p Fx(Li)o Fw(])f(and)f([)p Fx(F)-9 b(u)q Fw(]\).)67 b(Aubin)41 b([)p Fx(Au2)p Fw(])f(and)h(Tian)f([)p Fx(Ti)o Fw(])h(ha)m(v)m(e)35 1596 y(sho)m(wn)i(that)f(for)f(suitable)g (v)-5 b(alues)41 b(of)h(holomorphic)d(in)m(v)-5 b(arian)m(ts)41 b(of)g(the)h(metric,)h(there)g(exists)f(an)35 1735 y(E.K.)33 b(metric)f(on)g Fv(M)10 b Fw(.)35 1875 y(F)-8 b(or)24 b Fv(!)t(=)p Fw(2)p Fv(\031)k Fw(in)23 b Fv(C)630 1838 y Fr(1)670 1875 y Fw(\()p Fv(M)10 b Fw(\),)27 b Fu(Tian)-10 b('s)26 b(invariant)34 b Fv(\013)q Fw(\()p Fv(M)10 b Fw(\))25 b(is)f(the)h(suprem)m(um)g(of)f(the)h(set)g(of)f(the)h(real)f (n)m(um)m(b)s(ers)35 2043 y Fv(\013)j Fw(satisfying)f(the)g(follo)m (wing:)38 b(there)27 b(exists)g(a)f(constan)m(t)h Fv(C)33 b Fw(suc)m(h)28 b(that)e(the)g(inequalit)m(y)3259 1908 y Fp(Z)3314 2133 y Ft(M)3410 2043 y Fv(e)3455 2002 y Fo(\000)p Ft(\013')3633 2043 y Fs(\024)i Fv(C)35 2231 y Fw(holds)23 b(for)f(all)f(the)i Fv(C)781 2195 y Fo(1)879 2231 y Fw(functions)f Fv(')h Fw(with)g Fv(!)6 b Fw(+)r Fv(i@)p 1840 2150 41 4 v 5 w(@)g(')28 b(>)f Fw(0)c(and)g(sup)17 b Fv(')28 b Fs(\025)g Fw(0,)d(where)f Fv(!)31 b Fw(=)c Fv(i)17 b(g)3352 2246 y Ft(\025)p 3405 2208 31 3 v(\026)3456 2231 y Fv(dz)3556 2195 y Ft(\025)3588 2231 y Fs(^)r Fv(d)p 3724 2176 34 4 v(z)3768 2194 y Ft(\026)35 2370 y Fw(is)33 b(the)g(metric)e(form.)42 b(Suc)m(h)34 b(functions)f Fv(')f Fw(are)h(said)f Fv(!)t Fu(-admissible)p Fw(.)35 2510 y(In)h([)p Fx(Ti)p Fw(],)f(Tian)g(established)h(that)f(if)g Fv(\013)q Fw(\()p Fv(M)10 b Fw(\))28 b Fv(>)g(m=)p Fw(\()p Fv(m)22 b Fw(+)g(1\),)33 b Fv(m)f Fw(b)s(eing)g(the)h(dimension)f(of)g Fv(M)10 b Fw(,)33 b(there)35 2649 y(exists)42 b(an)f(E.K.)h(metric)d (on)i Fv(M)10 b Fw(.)70 b(This)41 b(condition)f(is)g(not)h(necessary:) 63 b(it)40 b(do)s(es)h(not)g(hold)g(on)f(the)35 2789 y(pro)5 b(jectiv)m(e)34 b(space,)g(where)g(Tian's)e(in)m(v)-5 b(arian)m(t)31 b(is)h(1)p Fv(=)p Fw(\()p Fv(m)22 b Fw(+)g(1\).)35 2928 y(In)33 b(the)g(same)f(pap)s(er,)g(Tian)g(in)m(tro)s(duces)h(a)f (more)f(restrictiv)m(e)i(in)m(v)-5 b(arian)m(t)31 b Fv(\013)2825 2943 y Ft(G)2884 2928 y Fw(\()p Fv(M)10 b Fw(\),)33 b(considering)e (only)35 3068 y(the)j(admissible)e(functions)h Fv(')g Fw(in)m(v)-5 b(arian)m(t)32 b(b)m(y)j(the)e(action)g(of)g(a)g(compact)g (group)g Fv(G)g Fw(of)g(holomorphic)35 3207 y(isometries.)69 b(The)42 b(su\016cien)m(t)h(condition)d(for)h(the)g(existence)i(of)e (an)g(E.K.)h(metric)e(on)i Fv(M)52 b Fw(remains)35 3347 y Fv(\013)97 3362 y Ft(G)157 3347 y Fw(\()p Fv(M)10 b Fw(\))28 b Fv(>)f(m=)p Fw(\()p Fv(m)c Fw(+)f(1\);)32 b(it)g(is)g(more)g(easily)g(satis\014ed)h(if)e(the)i(group)f Fv(G)h Fw(is)f(ric)m(h)g(enough.)35 3486 y(In)41 b(man)m(y)g(cases,)j (the)d(group)f Fv(G)h Fw(is)f(a)g(non-discrete)h(Lie)f(group.)67 b(The)41 b(in)m(v)-5 b(arian)m(t)40 b Fv(\013)3248 3501 y Ft(G)3307 3486 y Fw(\()p Fv(M)10 b Fw(\))41 b(can)g(b)s(e)35 3626 y(computed)27 b(using)g(subharmonic)f(functions)g(metho)s(ds)h (and)f(the)h(maxim)m(um)e(principle)g(\(for)h(e\013ectiv)m(e)35 3765 y(examples,)33 b(see)h([)p Fx(Be1)p Fw(],)e([)p Fx(Be2)p Fw(],)h([)p Fx(Be-Ch1)q Fw(],)f([)p Fx(Be-Ch2)q Fw(],)h([)p Fx(Re)o Fw(]\).)35 3904 y(In)g(this)g(pap)s(er,)f(w)m(e)i (pro)m(v)m(e)g(the)f(follo)m(wing)d(theorem:)35 4102 y Fi(Theorem)38 b(1.1)p Fw(.)43 b(|)49 b Fu(Tian)-10 b('s)33 b(invariant)i(on)f Fv(G)1817 4117 y Ft(p;q)1910 4102 y Fw(\()p Fq(C)j Fw(\))k Fu(is)34 b(given)g(by)h Fv(\013)18 b Fw(\()o Fv(G)2789 4117 y Ft(p;q)2883 4102 y Fw(\()p Fq(C)36 b Fw(\)\))e(=)27 b(1)p Fv(=)p Fw(\()p Fv(p)22 b Fw(+)g Fv(q)t Fw(\))p Fu(.)35 4300 y Fw(This)36 b(generalizes)e(the)i(kno)m(wn)g(result)f(on)g Fq(P)1704 4264 y Ft(m)1773 4300 y Fw(\()p Fq(C)i Fw(\))j(\([)p Fx(Ti)o Fw(],)c(see)h(also)d([)p Fx(Au3)p Fw(]\).)51 b(Let)35 b(us)h(also)e(men)m(tion)35 4439 y(that)29 b(Tian's)h(in)m(v) -5 b(arian)m(t)28 b(has)h(b)s(een)h(computed)g(on)f Fq(P)1980 4403 y Ft(m)2048 4439 y Fw(\()p Fq(C)37 b Fw(\))e(blo)m(wn)29 b(up)h(at)f(one)g(p)s(oin)m(t)g(and)g(on)g(certain)35 4579 y(F)-8 b(ermat)32 b(h)m(yp)s(ersurfaces)j(using)d(H\177)-49 b(ormander)32 b Fv(L)1814 4542 y Fr(2)1887 4579 y Fw(estimates)g(for)g (the)p 2633 4497 57 4 v 33 w Fv(@)6 b Fw(-equation)32 b(\([)p Fx(Ti)o Fw(]\).)35 4718 y(W)-8 b(e)45 b(\014rst)f(compute)g (the)h(v)m(olume)e(elemen)m(t)h(of)g(the)g(metric)11 b Fh(G)2435 4749 y Ft(p;q)2528 4718 y Fw(;)50 b(then)45 b(w)m(e)g(will)c(establish)j(some)35 4858 y(general)26 b(preliminary)e(results)i(concerning)h(Tian's)f(in)m(v)-5 b(arian)m(t)25 b(as)i(w)m(ell)e(as)h(im)m(b)s(eddings)g(of)3394 4777 y Fp(\010)3452 4858 y Fq(P)3511 4821 y Fr(1)3553 4858 y Fw(\()p Fq(C)37 b Fw(\))3712 4777 y Fp(\011)3775 4799 y Ft(p)35 4997 y Fw(in)32 b Fv(G)226 5012 y Ft(p;q)319 4997 y Fw(\()p Fq(C)37 b Fw(\))h(whic)m(h)33 b(allo)m(w)e(us)j(to)e (deduce)i Fv(\013)17 b Fw(\()p Fv(G)1811 5012 y Ft(p;q)1904 4997 y Fw(\()p Fq(C)37 b Fw(\)\))h(from)32 b Fv(\013)17 b Fw(\()p Fq(P)2546 4961 y Fr(1)2587 4997 y Fw(\()p Fq(C)37 b Fw(\)\))5 b(.)p eop %%Page: 3 3 3 2 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h (GRASSMANN)d(MANIF)n(OLD)804 b Fk(3)772 619 y Fx(2.)56 b(Basic)36 b(prop)s(erties)h(of)h(the)f(Grassmann)i(manifold)35 817 y Fw(W)-8 b(e)26 b(prop)s(ose)g(here)h(a)e(short)h(surv)m(ey)i(of)d (the)h(prop)s(erties)g(of)f(Grassmann)g(manifold)e(\(for)i(more)g (details,)35 956 y(see)40 b([)p Fx(Ko-No)p Fw(]\).)60 b(W)-8 b(e)39 b(denote)g(b)m(y)g Fv(G)1415 971 y Ft(p;q)1509 956 y Fw(\()p Fq(C)d Fw(\))44 b(the)39 b(set)g(of)f(the)g(subspaces)j (of)d(dimension)f Fv(p)h Fw(in)g Fq(C)3654 920 y Ft(p)p Fr(+)p Ft(q)3788 956 y Fw(;)35 1096 y(in)c(particular,)f Fv(G)707 1111 y Fr(1)p Ft(;m)828 1096 y Fw(\()p Fq(C)k Fw(\))j(is)34 b(the)h(complex)f(pro)5 b(jectiv)m(e)35 b(space)g(of)f(dimension)f Fv(m)p Fw(.)49 b(It)34 b(is)g(kno)m(wn)i (\(see)35 1235 y([)p Fx(Au3)p Fw(]\))h(that)f(on)h Fq(P)781 1250 y Ft(m)849 1235 y Fw(\()p Fq(C)g Fw(\),)43 b(the)37 b(F)-8 b(ubini-Study)35 b(metric)g(is)h(Einstein)h(with)f(factor)g Fv(m)25 b Fw(+)f(1)37 b(and)f(that)35 1375 y(Tian's)i(in)m(v)-5 b(arian)m(t)37 b(is)g(1)p Fv(=)p Fw(\()p Fv(m)25 b Fw(+)h(1\).)58 b(No)m(w,)40 b(let)d Fv(M)1883 1339 y Fo(\003)1923 1375 y Fw(\()p Fv(p)26 b Fw(+)f Fv(q)t(;)17 b(p)p Fw(\))37 b(b)s(e)h(the)h(set)f(of)f(the)h(matrices)f(of)h(rank)35 1514 y Fv(p)f Fw(in)e Fv(M)332 1529 y Ft(p)p Fr(+)p Ft(q)r(;p)516 1514 y Fw(\()p Fq(C)i Fw(\).)60 b(The)37 b(group)f Fv(Gl)1352 1529 y Ft(p)1391 1514 y Fw(\()p Fq(C)h Fw(\))42 b(acts)37 b(b)m(y)g(m)m(ultiplication)31 b(on)36 b(the)h(righ)m(t)e(on)h Fv(M)3358 1478 y Fo(\003)3398 1514 y Fw(\()p Fv(p)25 b Fw(+)f Fv(q)t(;)17 b(p)p Fw(\).)35 1654 y(More)31 b(precisely)682 1573 y Fp(\000)727 1654 y Fv(M)831 1618 y Fo(\003)872 1654 y Fw(\()p Fv(p)17 b Fw(+)h Fv(q)t(;)f(p)p Fw(\))p Fv(;)46 b(\031)t(;)h(G)1531 1669 y Ft(p;q)1624 1654 y Fw(\()p Fq(C)37 b Fw(\))1783 1573 y Fp(\001)1864 1654 y Fw(is)30 b(a)g(principal)e(\014b)s(er)j(bundle)g(with)f(group)g Fv(Gl)3584 1669 y Ft(p)3623 1654 y Fw(\()p Fq(C)37 b Fw(\).)35 1793 y(The)k(group)e Fv(Gl)632 1808 y Ft(p)p Fr(+)p Ft(q)760 1793 y Fw(\()p Fq(C)e Fw(\))45 b(acts)40 b(b)m(y)g(m)m(ultiplication)35 b(on)k(the)h(left)f(on)g Fv(M)2688 1757 y Fo(\003)2728 1793 y Fw(\()p Fv(p)27 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\))38 b(and)i(induces)g(an)35 1933 y(action)33 b(on)g Fv(G)542 1948 y Ft(p;q)635 1933 y Fw(\()p Fq(C)k Fw(\);)j(so)33 b(do)s(es)h(the)g(unitary)f(group)g Fv(U)10 b Fw(\()p Fv(p)24 b Fw(+)e Fv(q)t Fw(\).)46 b(These)35 b(groups)f(act)f(transitiv)m(ely)g(on)35 2072 y Fv(G)112 2087 y Ft(p;q)206 2072 y Fw(\()p Fq(C)j Fw(\),)j(whic)m(h)33 b(sho)m(ws)h(that)e Fv(G)1277 2087 y Ft(p;q)1370 2072 y Fw(\()p Fq(C)37 b Fw(\))h(is)32 b(compact.)35 2212 y(W)-8 b(e)36 b(denote)g(b)m(y)g Fs(I)43 b Fw(the)35 b(set)h(of)f(all)e(increasing-ordered)i(subsets)i(of)e Fv(p)g Fw(elemen)m(ts)g(in)f Fs(f)p Fw(1)p Fv(;)17 b(:)g(:)g(:)f(;)h(p) 23 b Fw(+)h Fv(q)t Fs(g)p Fw(.)35 2351 y(Let)43 b Fv(P)55 b Fw(b)s(e)43 b(an)f(elemen)m(t)f(of)h Fv(M)1220 2315 y Fo(\003)1260 2351 y Fw(\()p Fv(p)29 b Fw(+)f Fv(q)t(;)17 b(p)p Fw(\),)44 b Fv(P)58 b Fw(=)1969 2270 y Fp(\000)2015 2351 y Fv(p)2064 2366 y Ft(ij)2125 2270 y Fp(\001)2180 2360 y Fg(1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(p)p Fg(+)p Fe(q)2216 2416 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)2452 2351 y Fw(.)72 b(By)42 b(Cauc)m(h)m(y-Binet)i(form)m(ula)c(w)m(e)35 2523 y(get:)59 b(det)386 2442 y Fp(\000)448 2486 y Ft(t)461 2523 y Fv(P)p 554 2443 60 4 v 13 w(P)631 2442 y Fp(\001)717 2523 y Fw(=)832 2448 y Fp(P)938 2552 y Ft(I)5 b Fo(2I)1085 2523 y Fs(j)17 b Fw(det)f Fv(m)1366 2549 y Fe(I)1406 2523 y Fw(\()p Fv(P)e Fw(\))p Fs(j)1587 2486 y Fr(2)1625 2523 y Fw(,)42 b(where)f Fv(m)2068 2538 y Ft(I)2108 2523 y Fw(\()p Fv(P)14 b Fw(\))39 b(is)h(the)g(matrix)2905 2442 y Fp(\000)2951 2523 y Fv(p)3000 2538 y Ft(ij)3061 2442 y Fp(\001)3162 2532 y Fe(i)p Ff(2)p Fe(I)3116 2588 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)3317 2523 y Fw(.)65 b(The)41 b(form)35 2695 y Fv(!)t Fw(,)f(where)h Fv(!)h Fw(=)c Fv(i)17 b(@)p 779 2614 57 4 v 5 w(@)40 b Fw(log)17 b(det)1148 2614 y Fp(\000)1210 2659 y Ft(t)1223 2695 y Fv(P)p 1316 2615 60 4 v 13 w(P)1393 2614 y Fp(\001)1439 2695 y Fw(,)40 b(is)f(in)m(v)-5 b(arian)m(t)37 b(b)m(y)j(the)g(action)e (of)g Fv(Gl)2865 2710 y Ft(p)2905 2695 y Fw(\()p Fq(C)f Fw(\))44 b(on)39 b Fv(M)3354 2659 y Fo(\003)3395 2695 y Fw(\()p Fv(p)26 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\),)35 2835 y(and)32 b(so)f(it)f(pro)5 b(jects)32 b(on)m(to)f(a)g(form)o Fh(G)1420 2865 y Ft(p;q)1513 2835 y Fw(.)43 b(The)32 b(metric)o Fh(G)2169 2865 y Ft(p;q)2294 2835 y Fw(is)e(a)h(K\177)-49 b(ahler)30 b(metric)g(form)g(on)h Fv(G)3530 2850 y Ft(p;q)3623 2835 y Fw(\()p Fq(C)37 b Fw(\).)35 2974 y(F)-8 b(or)34 b Fv(p)c Fw(=)h(1,)j(this)g(metric)f(on)h Fv(G)1219 2989 y Fr(1)p Ft(;m)1340 2974 y Fw(\()p Fq(C)j Fw(\))j(is)34 b(the)g(F)-8 b(ubini-Study)33 b(metric)h(on)g(the)g(complex)g(pro)5 b(jectiv)m(e)35 3114 y(space.)45 b(The)33 b(action)f(of)g(the)h (unitary)e(group)i Fv(U)10 b Fw(\()p Fv(p)22 b Fw(+)g Fv(q)t Fw(\))32 b(on)g Fv(G)2338 3129 y Ft(p;q)2431 3114 y Fw(\()p Fq(C)37 b Fw(\))h(preserv)m(es)d(the)e(metric)p Fh(G)3602 3144 y Ft(p;q)3728 3114 y Fw(so)35 3253 y(that)27 b Fv(U)10 b Fw(\()p Fv(p)h Fw(+)g Fv(q)t Fw(\))26 b(is)h(a)f(group)h (of)g(holomorphic)d(isometries)i(whic)m(h)h(op)s(erates)g(transitiv)m (ely)g(on)f Fv(G)3530 3268 y Ft(p;q)3623 3253 y Fw(\()p Fq(C)37 b Fw(\).)35 3393 y(F)-8 b(or)36 b Fv(I)45 b Fw(in)36 b Fs(I)7 b Fw(,)38 b(let)e Fv(U)757 3408 y Ft(I)834 3393 y Fw(b)s(e)h(the)g(set)h(of)e(the)h(matrices)f Fv(P)50 b Fw(in)36 b Fv(M)2317 3356 y Fo(\003)2357 3393 y Fw(\()p Fv(p)25 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\))36 b(suc)m(h)i(that)f(det\()p Fv(m)3482 3408 y Ft(I)3522 3393 y Fw(\()p Fv(P)14 b Fw(\)\))36 b(is)35 3532 y(non-zero.)53 b(Then)37 b Fv(\031)t Fw(\()p Fv(U)899 3547 y Ft(I)939 3532 y Fw(\))f(is)f(a)g(co)s(ordinate)g(op)s (en)h(set)g(on)f Fv(G)2290 3547 y Ft(p;q)2384 3532 y Fw(\()p Fq(C)h Fw(\),)42 b(the)37 b(matrix)d Fv(Z)3170 3547 y Ft(I)3245 3532 y Fw(in)h Fv(M)3456 3547 y Ft(p;q)3549 3532 y Fw(\()p Fq(C)i Fw(\))k(is)35 3671 y(the)f(co)s(ordinate,)g(the)g (in)m(v)m(erse)h(of)e(the)g(c)m(hart)h Fv(')1845 3686 y Ft(I)1924 3671 y Fw(sends)h Fv(M)2296 3635 y Fo(\003)2336 3671 y Fw(\()p Fv(p)27 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\))38 b(on)m(to)i Fv(\031)t Fw(\()p Fv(U)3159 3686 y Ft(I)3199 3671 y Fw(\))f(and)g(w)m(e)i(ha)m(v)m(e)35 3811 y Fv(m)120 3826 y Ft(I)161 3730 y Fp(\000)206 3811 y Fv(')270 3770 y Fo(\000)p Fr(1)270 3838 y Ft(I)365 3811 y Fw(\()p Fv(Z)470 3826 y Ft(I)509 3811 y Fw(\))547 3730 y Fp(\001)620 3811 y Fw(=)28 b Fv(I)775 3775 y Fr(\()p Ft(p)p Fr(\))902 3811 y Fw(where)34 b Fv(I)1235 3775 y Fr(\()p Ft(p)p Fr(\))1362 3811 y Fw(is)e(the)h Fv(p)22 b Fs(\002)h Fv(p)32 b Fw(iden)m(tit)m(y)g(matrix,)g(and)g Fv(m)2859 3826 y Ft(I)2895 3807 y Fe(c)2931 3730 y Fp(\000)2977 3811 y Fv(')3041 3770 y Fo(\000)p Fr(1)3041 3838 y Ft(I)3135 3811 y Fw(\()p Fv(Z)3240 3826 y Ft(I)3280 3811 y Fw(\))3318 3730 y Fp(\001)3391 3811 y Fw(=)c Fv(Z)3562 3826 y Ft(I)3602 3811 y Fw(.)35 4009 y Fi(Lemma)39 b(2.1)p Fw(.)k(|)48 b Fu(F)-7 b(or)34 b Fv(I)43 b Fu(in)34 b Fs(I)7 b Fu(,)35 b(let)g Fv(\025)1472 4024 y Ft(I)1547 4009 y Fu(b)-5 b(e)35 b(the)g(map)f(fr)-5 b(om)34 b Fv(\031)t Fw(\()p Fv(U)2436 4024 y Ft(I)2476 4009 y Fw(\))h Fu(to)g Fq(R)2732 4024 y Fr(+)2832 4009 y Fu(de\014ne)-5 b(d)34 b(by)1216 4199 y Fv(\025)1273 4214 y Ft(I)1313 4199 y Fw(\()p Fv(Z)1418 4214 y Ft(I)1457 4199 y Fw(\))28 b(=)1626 4114 y Fp(\014)1626 4174 y(\014)1676 4199 y Fw(det)q(\(Id)17 b(+)2032 4158 y Ft(t)2061 4199 y Fv(Z)2128 4214 y Ft(I)p 2184 4119 58 4 v 2167 4199 a Fv(Z)2242 4214 y Ft(I)2282 4199 y Fw(\))2337 4114 y Fp(\014)2337 4174 y(\014)2369 4140 y Fo(\000)p Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2608 4199 y Fv(:)35 4387 y Fu(Then)289 4306 y Fp(\000)335 4387 y Fv(\025)392 4402 y Ft(I)432 4306 y Fp(\001)478 4426 y Ft(I)5 b Fo(2I)643 4387 y Fu(ar)-5 b(e)35 b(the)f(c)-5 b(omp)g(onents)34 b(of)h(a)f(maximal)g(di\013er)-5 b(ential)34 b(form)g Fv(\021)39 b Fu(on)34 b Fv(G)3119 4402 y Ft(p;q)3212 4387 y Fw(\()p Fq(C)j Fw(\))p Fu(,)j(namely:)1381 4575 y Fv(\021)31 b Fw(=)d Fv(\025)1621 4590 y Ft(I)1661 4495 y Fp(\000)1706 4575 y Fv(i=)p Fw(2)1837 4495 y Fp(\001)1883 4517 y Ft(pq)1973 4495 y Fp(\000)2019 4575 y Fv(d)-5 b(Z)13 b Fs(^)21 b Fv(d)p 2300 4495 V(Z)2357 4495 y Fp(\001)2402 4614 y Ft(I)2442 4575 y Fv(:)35 4773 y Fu(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(It)33 b(su\016ces)i(to)d(sho)m(w)h(that)g(the)g(follo)m (wing)d(transformation)g(rule)i(holds:)423 5010 y(for)g(ev)m(ery)j Fv(I)8 b(;)946 4985 y Fp(e)940 5010 y Fv(I)41 b Fw(in)32 b Fs(I)7 b Fv(;)49 b(\025)1332 5025 y Ft(I)1405 5010 y Fw(is)32 b(equal)g(to)g Fv(\025)1940 5024 y Fd(e)1936 5041 y Ft(I)1998 5010 y Fs(\002)2098 4866 y Fp(\014)2098 4926 y(\014)2098 4986 y(\014)2098 5045 y(\014)2148 5010 y Fw(det)2343 4941 y Fv(@)23 b(Z)2488 4955 y Fd(e)2484 4972 y Ft(I)p 2343 4988 181 4 v 2343 5079 a Fv(@)g(Z)2484 5094 y Ft(I)2550 4866 y Fp(\014)2550 4926 y(\014)2550 4986 y(\014)2550 5045 y(\014)2583 4892 y Fr(2)2672 5010 y Fw(on)32 b Fv(\031)t Fw(\()p Fv(U)2970 5025 y Ft(I)3010 5010 y Fw(\))22 b Fs(\\)h Fv(\031)t Fw(\()p Fv(U)3326 5024 y Fd(e)3322 5041 y Ft(I)3362 5010 y Fw(\))p Fv(:)35 5263 y Fw(Let)34 b Fv(P)274 5278 y Ft(I)347 5263 y Fw(b)s(e)f(the)h (matrix)d Fv(')1030 5222 y Fo(\000)p Fr(1)1030 5290 y Ft(I)1125 5263 y Fw(\()p Fv(Z)1230 5278 y Ft(I)1269 5263 y Fw(\).)46 b(Then)34 b Fv(P)1698 5278 y Ft(I)1738 5183 y Fp(\010)1796 5263 y Fv(m)1885 5277 y Fd(e)1881 5294 y Ft(I)1921 5263 y Fw(\()p Fv(P)2022 5278 y Ft(I)2062 5263 y Fw(\))2100 5183 y Fp(\011)2158 5205 y Fo(\000)p Fr(1)2281 5263 y Fw(=)28 b Fv(P)2452 5277 y Fd(e)2448 5294 y Ft(I)2488 5263 y Fw(,)34 b(so)f Fv(Z)2740 5277 y Fd(e)2736 5294 y Ft(I)2804 5263 y Fw(=)c Fv(m)3014 5273 y Fr(~)3006 5290 y Ft(I)3042 5272 y Fe(c)3078 5263 y Fw(\()p Fv(P)3179 5278 y Ft(I)3219 5263 y Fw(\))3274 5183 y Fp(\010)3331 5263 y Fv(m)3420 5277 y Fd(e)3416 5294 y Ft(I)3457 5263 y Fw(\()p Fv(P)3558 5278 y Ft(I)3597 5263 y Fw(\))3635 5183 y Fp(\011)3694 5205 y Fo(\000)p Fr(1)3788 5263 y Fw(.)35 5403 y(The)j(di\013eren)m(tial)d(of)h(the)i (map)e(whic)m(h)h(sends)h Fv(Z)1814 5418 y Ft(I)1885 5403 y Fw(on)e Fv(P)2081 5418 y Ft(I)2152 5403 y Fw(is)g(the)h(map)f (whic)m(h)i(sends)g Fv(H)38 b Fw(on)3444 5378 y(\025)3419 5403 y Fv(H)7 b Fw(,)32 b(where)p eop %%Page: 4 4 4 3 bop 35 283 a Fk(4)1490 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 619 y Fv(m)132 634 y Ft(I)168 615 y Fe(c)204 619 y Fw(\()268 594 y(\025)242 619 y Fv(H)8 b Fw(\))28 b(=)f Fv(H)40 b Fw(and)33 b Fv(m)896 634 y Ft(I)936 619 y Fw(\()999 594 y(\025)974 619 y Fv(H)8 b Fw(\))27 b(=)h(0.)43 b(The)33 b(c)m(hange)h(of)e(c)m(harts)h(sending)g Fv(Z)2695 634 y Ft(I)2767 619 y Fw(on)g Fv(Z)2974 633 y Fd(e)2970 650 y Ft(I)3010 619 y Fw(,)f(w)m(e)i(obtain)342 808 y Fv(D)19 b(Z)513 822 y Fd(e)509 839 y Ft(I)549 808 y Fw(\()p Fv(H)8 b Fw(\))27 b(=)g Fv(m)950 818 y Fr(~)941 835 y Ft(I)977 816 y Fe(c)1013 808 y Fw(\()1077 783 y(\025)1051 808 y Fv(H)8 b Fw(\))1195 727 y Fp(\010)1252 808 y Fv(m)1341 822 y Fd(e)1337 839 y Ft(I)1378 808 y Fw(\()p Fv(P)1479 823 y Ft(I)1518 808 y Fw(\))1556 727 y Fp(\011)1615 750 y Fo(\000)p Fr(1)1731 808 y Fs(\000)23 b Fv(m)1936 818 y Fr(~)1928 835 y Ft(I)1964 816 y Fe(c)2000 808 y Fw(\()p Fv(P)2101 823 y Ft(I)2140 808 y Fw(\))2195 727 y Fp(\010)2253 808 y Fv(m)2342 822 y Fd(e)2338 839 y Ft(I)2378 808 y Fw(\()p Fv(P)2479 823 y Ft(I)2519 808 y Fw(\))2557 727 y Fp(\011)2615 750 y Fo(\000)p Fr(1)2726 808 y Fv(m)2815 822 y Fd(e)2811 839 y Ft(I)2851 808 y Fw(\()2915 783 y(\025)2889 808 y Fv(H)8 b Fw(\))3033 727 y Fp(\010)3090 808 y Fv(m)3179 822 y Fd(e)3175 839 y Ft(I)3216 808 y Fw(\()p Fv(P)3317 823 y Ft(I)3356 808 y Fw(\))3394 727 y Fp(\011)3452 750 y Fo(\000)p Fr(1)741 992 y Fw(=)844 911 y Fp(\000)890 992 y Fv(m)995 1002 y Fr(~)987 1019 y Ft(I)1023 1000 y Fe(c)1059 992 y Fw(\()1122 966 y(\025)1097 992 y Fv(H)f Fw(\))23 b Fs(\000)f Fv(\015)g(m)1507 1006 y Fd(e)1503 1022 y Ft(I)1543 992 y Fw(\()1606 966 y(\025)1581 992 y Fv(H)8 b Fw(\))1708 911 y Fp(\001)1770 992 y Fv(\013)1833 950 y Fo(\000)p Fr(1)1927 992 y Fv(;)304 1166 y Fw(where)98 b Fv(\013)29 b Fw(=)e Fv(m)933 1180 y Fd(e)929 1196 y Ft(I)970 1166 y Fw(\()p Fv(P)1071 1181 y Ft(I)1110 1166 y Fw(\))p Fv(;)50 b(\014)33 b Fw(=)27 b Fv(m)1521 1176 y Fr(~)1513 1193 y Ft(I)1549 1174 y Fe(c)1585 1166 y Fw(\()p Fv(P)1686 1181 y Ft(I)1726 1166 y Fw(\))33 b(and)f Fv(\015)h Fw(=)27 b Fv(\014)c(\013)2314 1125 y Fo(\000)p Fr(1)2408 1166 y Fv(:)35 1363 y Fw(Let)43 b(us)g(de\014ne)g(a)g(map)e Fv(u)h Fw(from)f Fv(M)1396 1378 y Ft(q)r(;p)1489 1363 y Fw(\()p Fq(C)c Fw(\))48 b(to)42 b Fv(M)1919 1378 y Ft(q)r(;p)2013 1363 y Fw(\()p Fq(C)37 b Fw(\))47 b(b)m(y)d Fv(u)p Fw(\()p Fv(H)8 b Fw(\))43 b(=)h Fv(m)2854 1373 y Fr(~)2846 1390 y Ft(I)2882 1372 y Fe(c)2918 1363 y Fw(\()2981 1338 y(\025)2956 1363 y Fv(H)8 b Fw(\))28 b Fs(\000)i Fv(\015)21 b(m)3379 1377 y Fd(e)3375 1394 y Ft(I)3415 1363 y Fw(\()3479 1338 y(\025)3453 1363 y Fv(H)8 b Fw(\).)73 b(W)-8 b(e)35 1503 y(can)45 b(c)m(ho)s(ose)f Fv(I)55 b Fw(=)47 b Fs(f)p Fv(q)33 b Fw(+)d(1)p Fv(;)17 b(:)g(:)g(:)e(;)i(q)34 b Fw(+)29 b Fv(p)p Fs(g)44 b Fw(and)1781 1478 y Fp(e)1775 1503 y Fv(I)55 b Fw(=)46 b Fs(f)p Fw(1)p Fv(;)17 b(:)g(:)g(:)f(;)h(r)s Fs(g)29 b([)h(f)p Fv(q)j Fw(+)d(1)g(+)f Fv(r)m(;)17 b(:)g(:)g(:)f(;)h(q)34 b Fw(+)29 b Fv(p)p Fs(g)p Fw(,)47 b(where)35 1642 y(0)28 b Fs(\024)g Fv(r)i Fs(\024)f Fw(inf)6 b(\()p Fv(p;)17 b(q)t Fw(\).)42 b(W)-8 b(e)33 b(de\014ne)h(the)f Fv(k)25 b Fs(\002)e Fv(l)35 b Fw(matrix)c Fv(E)2053 1591 y Fr(\()p Ft(k)r Fo(\002)p Ft(l)q Fr(\))2047 1668 y Ft(i;j)2260 1642 y Fw(b)m(y)2395 1562 y Fp(\000)2441 1642 y Fv(E)2519 1591 y Fr(\()p Ft(k)r Fo(\002)p Ft(l)q Fr(\))2513 1668 y Ft(i;j)2693 1562 y Fp(\001)2739 1681 y Ft(\025\026)2854 1642 y Fw(=)d Fv(\016)3001 1657 y Ft(i\025)3087 1642 y Fv(\016)3130 1657 y Ft(j)t(\026)3209 1642 y Fw(.)44 b(W)-8 b(e)33 b(ha)m(v)m(e)606 1852 y Fv(m)695 1866 y Fd(e)691 1883 y Ft(I)731 1771 y Fp(\000)800 1827 y Fw(\025)777 1852 y Fv(E)855 1801 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))849 1878 y Ft(i;j)1038 1771 y Fp(\001)1112 1852 y Fw(=)27 b Fv(E)1293 1801 y Fr(\()p Ft(p)p Fo(\002)p Ft(p)p Fr(\))1287 1878 y Ft(i;j)1576 1852 y Fw(if)k Fv(i)d Fs(\024)g Fv(r)m(;)50 b Fw(and)32 b(0)h(if)e Fv(i)d(>)g(r)m(;)307 2042 y Fw(and)98 b Fv(m)667 2052 y Fr(~)659 2069 y Ft(I)695 2050 y Fe(c)731 1961 y Fp(\000)800 2017 y Fw(\025)777 2042 y Fv(E)855 1991 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))849 2068 y Ft(i;j)1038 1961 y Fp(\001)1112 2042 y Fw(=)27 b Fv(E)1293 1991 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))1287 2068 y Ft(i)p Fo(\000)p Ft(r)n(;j)1574 2042 y Fw(if)k Fv(i)d(>)g(r)m(;)49 b Fw(and)33 b(0)f(if)g Fv(i)c Fs(\024)g Fv(r)m(:)33 b Fw(Hence)365 2151 y Fp(\000)411 2232 y Fv(\015)21 b(m)572 2246 y Fd(e)568 2262 y Ft(I)608 2232 y Fw(\()669 2207 y(\025)646 2232 y Fv(E)724 2181 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))718 2257 y Ft(i;j)908 2232 y Fw(\))946 2151 y Fp(\001)991 2271 y Ft(\013\014)1112 2232 y Fw(=)27 b Fv(\015)1266 2247 y Ft(\013i)1356 2232 y Fv(m)1445 2246 y Fd(e)1441 2262 y Ft(I)1481 2232 y Fw(\()1542 2207 y(\025)1519 2232 y Fv(E)1597 2181 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))1591 2257 y Ft(i;j)1780 2232 y Fw(\))1818 2247 y Ft(ij)1895 2232 y Fv(\016)1938 2247 y Ft(j)t(\014)2046 2232 y Fw(=)g Fv(\015)2200 2247 y Ft(\013i)2290 2232 y Fv(\016)2333 2247 y Ft(j)t(\014)2510 2232 y Fw(if)32 b Fv(i)c Fs(\024)g Fv(r)m(;)49 b Fw(and)33 b(0)f(elsewhere)r Fv(:)35 2435 y Fw(No)m(w)44 b(the)g(map)f(whic)m(h)h(sends)h Fv(H)51 b Fw(to)43 b Fv(\015)22 b(m)1661 2449 y Fd(e)1657 2466 y Ft(I)1697 2435 y Fw(\()1760 2410 y(\025)1735 2435 y Fv(H)7 b Fw(\))44 b(can)g(b)s(e)f(restricted)h(if)e(1)k Fs(\024)h Fv(j)52 b Fs(\024)47 b Fv(p)c Fw(to)g(the)h(span)35 2575 y Fv(B)109 2590 y Ft(j)188 2575 y Fw(of)d(the)485 2494 y Fp(\000)531 2575 y Fv(E)603 2590 y Ft(i;j)683 2494 y Fp(\001)729 2614 y Fr(1)p Fo(\024)p Ft(i)p Fo(\024)p Ft(q)936 2575 y Fw(.)71 b(The)42 b Fv(r)j Fw(\014rst)d(columns)f(of)g (its)g(matrix)f(are)i(those)g(of)f Fv(\015)5 b Fw(,)44 b(the)f(others)f(are)35 2729 y(0.)87 b(The)48 b(map)e(whic)m(h)i(sends) h Fv(H)54 b Fw(to)47 b Fv(\015)21 b(m)1661 2739 y Fr(~)1652 2756 y Ft(I)1688 2738 y Fe(c)1724 2729 y Fw(\()1788 2704 y(\025)1762 2729 y Fv(H)8 b Fw(\))47 b(maps)g(also)f Fv(B)2490 2744 y Ft(j)2573 2729 y Fw(in)m(to)h(itself.)85 b(The)48 b(righ)m(t)e(upp)s(er)35 2869 y(blo)s(c)m(k)c(of)g(its)g (matrix)f(is)g Fv(I)1054 2833 y Fr(\()p Ft(q)r Fo(\000)p Ft(r)r Fr(\))1236 2869 y Fw(,)j(the)f(other)f(elemen)m(ts)h(are)f(0.)72 b(This)42 b(allo)m(ws)g(us)g(to)g(compute)g(the)35 3008 y(matrix)d(of)g(the)h(restriction)f(of)g Fv(u)g Fw(to)g Fv(B)1540 3023 y Ft(j)1577 3008 y Fw(,)i(whose)g(determinan)m(t)f(is)f (\()p Fs(\000)p Fw(1\))2805 2972 y Ft(r)r Fo(\002)p Fr(\()p Ft(q)r Fo(\000)p Ft(r)r Fr(\))3092 3008 y Fw(det)3227 2928 y Fp(\000)3273 3008 y Fv(\015)3324 3023 y Ft(ij)3384 2928 y Fp(\001)3440 3017 y Fe(q)r Ff(\000)p Fe(r)r Fg(+1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)3514 3073 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(r)3788 3008 y Fw(.)35 3209 y(So)g(det)17 b Fv(u)38 b Fw(=)g(\()p Fs(\000)p Fw(1\))739 3173 y Ft(p)p Fo(\002)p Ft(r)r Fo(\002)p Fr(\()p Ft(q)r Fo(\000)p Ft(r)r Fr(\))1116 3098 y Fp(h)1163 3209 y Fw(det)1299 3128 y Fp(\000)1344 3209 y Fv(\015)1395 3224 y Ft(i)12 b(j)1467 3128 y Fp(\001)1523 3218 y Fe(q)r Ff(\000)p Fe(r)r Fg(+1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)1597 3274 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(r)1871 3098 y Fp(i)1918 3120 y Ft(p)1958 3209 y Fw(.)62 b(F)-8 b(or)38 b(1)g Fs(\024)g Fv(i)h Fs(\024)f Fv(q)t Fw(,)i(let)e Fv(C)2948 3224 y Ft(i)3015 3209 y Fw(b)s(e)h(the)g(span)g(of)f(the)35 3367 y(\()p Fv(E)145 3382 y Ft(i;j)226 3367 y Fw(\))264 3382 y Fr(1)p Fo(\024)p Ft(j)t Fo(\024)p Ft(p)481 3367 y Fw(.)65 b(Eac)m(h)41 b Fv(C)893 3382 y Ft(i)961 3367 y Fw(is)e(stable)g(b)m(y)i(the)f(map)g (from)e Fv(M)2229 3382 y Ft(q)r(;p)2323 3367 y Fw(\()p Fq(C)f Fw(\))45 b(to)39 b Fv(M)2747 3382 y Ft(q)r(;p)2841 3367 y Fw(\()p Fq(C)e Fw(\))45 b(whic)m(h)40 b(sends)i Fv(H)47 b Fw(to)35 3506 y Fv(H)25 b(\013)204 3470 y Fo(\000)p Fr(1)298 3506 y Fw(.)48 b(The)35 b(matrix)d(of)i(the)g(restriction)g (is)f Fv(\013)1806 3470 y Fo(\000)p Fr(1)1900 3506 y Fw(,)i(so)f(the)h(determinan)m(t)e(of)h(the)g(map)g(is)f(\(det)17 b Fv(\013)q Fw(\))3695 3470 y Fo(\000)p Ft(q)3788 3506 y Fw(.)35 3646 y(Hence)793 3701 y Fp(\014)793 3760 y(\014)843 3785 y Fw(det)g Fv(D)s(Z)1150 3799 y Fd(e)1146 3816 y Ft(I)1185 3785 y Fw(\()p Fv(H)8 b Fw(\))1367 3701 y Fp(\014)1367 3760 y(\014)1400 3727 y Fr(2)1467 3785 y Fw(=)1570 3701 y Fp(\014)1570 3760 y(\014)1620 3785 y Fw(det)17 b(\()p Fv(\015)1861 3800 y Ft(i;j)1941 3785 y Fw(\))1989 3812 y Fe(q)r Ff(\000)p Fe(r)r Fg(+1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)2063 3865 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(r)2358 3701 y Fp(\014)2358 3760 y(\014)2391 3727 y Fr(2)p Ft(p)2488 3785 y Fs(\002)2588 3701 y Fp(\014)2588 3760 y(\014)2637 3785 y Fw(det)h Fv(\013)2869 3701 y Fp(\014)2869 3760 y(\014)2902 3727 y Fo(\000)p Fr(2)p Ft(q)3030 3785 y Fv(:)35 3982 y Fw(Let)39 b Fv(A)f Fw(b)s(e)h(the)g(righ)m(t)e Fv(r)29 b Fs(\002)e Fv(r)41 b Fw(upp)s(er)e(blo)s(c)m(k)f(of)g Fv(\013)q Fw(.)60 b(The)40 b(left)d(\()p Fv(p)26 b Fs(\000)h Fv(r)s Fw(\))f Fs(\002)g Fw(\()p Fv(p)g Fs(\000)h Fv(r)s Fw(\))38 b(lo)m(w)m(er)g(blo)s(c)m(k)g(of)g Fv(\013)35 4122 y Fw(is)e Fv(I)188 4085 y Fr(\()p Ft(p)p Fo(\000)p Ft(r)r Fr(\))407 4122 y Fw(and)g(the)g(righ)m(t)g(\()p Fv(p)24 b Fs(\000)h Fv(r)s Fw(\))f Fs(\002)h Fv(r)38 b Fw(lo)m(w)m(er)f(blo)s(c)m(k)e(is)h(0,)g(so)h(det)17 b Fv(\013)34 b Fw(=)f(\()p Fs(\000)p Fw(1\))2933 4085 y Ft(r)r Fr(\()p Ft(p)p Fo(\000)p Ft(r)r Fr(\))3167 4122 y Fw(det)17 b Fv(A)p Fw(.)54 b(The)37 b(left)35 4261 y Fv(r)26 b Fs(\002)e Fw(\()p Fv(p)f Fs(\000)h Fv(r)s Fw(\))34 b(lo)m(w)m(er)g(blo)s(c)m(k)g(of)g Fv(\014)40 b Fw(is)34 b(0,)g(the)h(righ)m(t)e Fv(r)26 b Fs(\002)e Fv(r)37 b Fw(blo)s(c)m(k)d(is)g Fv(I)2538 4225 y Fr(\()p Ft(r)r Fr(\))2665 4261 y Fw(so)g(that)g(the)h(left)e Fv(r)26 b Fs(\002)e Fv(r)37 b Fw(lo)m(w)m(er)35 4401 y(blo)s(c)m(k)c(of)f Fv(\015)37 b Fw(is)c Fv(A)664 4364 y Fo(\000)p Fr(1)758 4401 y Fw(.)35 4540 y(F)-8 b(rom)31 b(this)i(w)m(e)g(deduce)950 4455 y Fp(\014)950 4515 y(\014)984 4540 y Fw(det)g Fv(D)s(Z)1307 4554 y Fd(e)1303 4571 y Ft(I)1343 4540 y Fw(\()p Fv(H)8 b Fw(\))1508 4455 y Fp(\014)1508 4515 y(\014)1540 4482 y Fr(2)1608 4540 y Fw(=)1711 4455 y Fp(\014)1711 4515 y(\014)1761 4540 y Fw(det)17 b Fv(\013)1992 4455 y Fp(\014)1992 4515 y(\014)2025 4482 y Fo(\000)p Fr(2\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2299 4540 y Fw(.)43 b(Since)33 b Fv(P)2687 4555 y Ft(I)2744 4540 y Fv(\013)2807 4504 y Fo(\000)p Fr(1)2928 4540 y Fw(=)28 b Fv(P)3099 4554 y Fd(e)3095 4571 y Ft(I)3135 4540 y Fw(,)k(w)m(e)i(ha)m(v)m(e)607 4793 y Fv(\025)668 4807 y Fd(e)664 4823 y Ft(I)731 4793 y Fw(=)835 4678 y Fp(\014)835 4738 y(\014)835 4798 y(\014)884 4793 y Fw(det)1020 4712 y Fp(\000)1082 4752 y Ft(t)1095 4793 y Fv(P)1162 4807 y Fd(e)1158 4823 y Ft(I)p 1215 4713 60 4 v 1198 4793 a Fv(P)1279 4807 y Fd(e)1275 4823 y Ft(I)1331 4712 y Fp(\001)1393 4678 y(\014)1393 4738 y(\014)1393 4798 y(\014)1427 4705 y Fo(\000)p Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))1692 4793 y Fw(=)1796 4708 y Fp(\014)1796 4768 y(\014)1846 4793 y Fw(det)17 b Fv(\013)2077 4708 y Fp(\014)2077 4768 y(\014)2110 4735 y Fr(2\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2329 4793 y Fv(\025)2386 4808 y Ft(I)2453 4793 y Fw(=)2557 4649 y Fp(\014)2557 4708 y(\014)2557 4768 y(\014)2557 4828 y(\014)2607 4793 y Fw(det)2786 4724 y Fv(@)5 b(Z)2913 4738 y Fd(e)2909 4754 y Ft(I)p 2786 4770 164 4 v 2786 4861 a Fv(@)g(Z)2909 4876 y Ft(I)2976 4649 y Fp(\014)2976 4708 y(\014)2976 4768 y(\014)2976 4828 y(\014)3009 4675 y Fo(\000)p Fr(2)3120 4793 y Fv(\025)3177 4808 y Ft(I)3217 4793 y Fv(:)p 3744 5011 4 66 v 3748 4948 59 4 v 3748 5011 V 3806 5011 4 66 v 35 5208 a Fi(Lemma)39 b(2.2)p Fw(.)k(|)48 b Fu(The)34 b(unitary)i(gr)-5 b(oup)34 b Fv(U)10 b Fw(\()p Fv(p)23 b Fw(+)f Fv(q)t Fw(\))35 b Fu(pr)-5 b(eserves)34 b Fv(\021)t Fu(.)p eop %%Page: 5 5 5 4 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h (GRASSMANN)d(MANIF)n(OLD)804 b Fk(5)35 619 y Fu(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(W)-8 b(e)27 b(call)e Fv(I)34 b Fw(the)27 b(set)g Fs(f)p Fv(q)13 b Fw(+)d(1)p Fv(;)17 b(:)g(:)g(:)e(;)i(q)c Fw(+)d Fv(p)p Fs(g)p Fw(.)41 b(W)-8 b(e)26 b(de\014ne)i Fv(P)2459 634 y Ft(I)2525 619 y Fw(in)e Fv(\031)t Fw(\()p Fv(U)2796 634 y Ft(I)2836 619 y Fw(\))g(b)m(y)h Fv(P)3092 634 y Ft(I)3160 619 y Fw(=)h Fv(')3328 578 y Fo(\000)p Fr(1)3328 646 y Ft(I)3422 619 y Fw(\()p Fv(Z)3527 634 y Ft(I)3566 619 y Fw(\).)42 b(Let)35 759 y Fv(U)c Fw(b)s(e)28 b(an)f(elemen)m(t)g(in)g Fv(U)10 b Fw(\()p Fv(p)h Fw(+)g Fv(q)t Fw(\))28 b(suc)m(h)h(that)e Fv(m)1741 774 y Ft(I)1782 759 y Fw(\()p Fv(U)10 b(P)1959 774 y Ft(I)1999 759 y Fw(\))27 b(is)g(in)m(v)m(ertible.)41 b(Let)2816 734 y(~)2794 759 y Fv(P)2857 774 y Ft(I)2924 759 y Fw(=)28 b Fv(U)10 b(P)3167 774 y Ft(I)3224 678 y Fp(\010)3282 759 y Fv(m)3367 774 y Ft(I)3407 759 y Fw(\()p Fv(U)g(P)3584 774 y Ft(I)3625 759 y Fw(\))3663 678 y Fp(\011)3721 700 y Fo(\000)p Fr(1)35 903 y Fw(and)246 878 y(~)225 903 y Fv(Z)292 918 y Ft(I)359 903 y Fw(=)28 b Fv(m)548 918 y Ft(I)584 899 y Fe(c)620 903 y Fw(\()680 878 y(~)658 903 y Fv(P)721 918 y Ft(I)761 903 y Fw(\).)43 b(W)-8 b(e)33 b(ha)m(v)m(e)1283 878 y(~)1262 903 y Fv(Z)1329 918 y Ft(I)1397 903 y Fw(=)27 b Fv(m)1585 918 y Ft(I)1621 899 y Fe(c)1657 903 y Fw(\()p Fv(U)10 b Fw(\))17 b Fv(P)1889 918 y Ft(I)1946 822 y Fp(\010)2004 903 y Fv(m)2089 918 y Ft(I)2129 903 y Fw(\()p Fv(U)10 b Fw(\))p Fv(P)2344 918 y Ft(I)2385 822 y Fp(\011)2443 845 y Fo(\000)p Fr(1)2537 903 y Fw(.)44 b(So)215 1110 y Fv(D)320 1085 y Fw(~)299 1110 y Fv(Z)366 1125 y Ft(I)406 1110 y Fw(\()p Fv(H)8 b Fw(\))27 b(=)g Fv(m)786 1125 y Ft(I)822 1106 y Fe(c)859 1110 y Fw(\()p Fv(U)10 b Fw(\))1028 999 y Fp(h)1100 1085 y Fw(\025)1075 1110 y Fv(H)1163 1029 y Fp(\010)1221 1110 y Fv(m)1306 1125 y Ft(I)1347 1110 y Fw(\()p Fv(U)g Fw(\))p Fv(P)1562 1125 y Ft(I)1602 1029 y Fp(\011)1660 1051 y Fo(\000)p Fr(1)1777 1110 y Fs(\000)22 b Fv(P)1939 1125 y Ft(I)1979 1029 y Fp(\010)2037 1110 y Fv(m)2122 1125 y Ft(I)2162 1110 y Fw(\()p Fv(U)10 b Fw(\))p Fv(P)2377 1125 y Ft(I)2418 1029 y Fp(\011)2476 1051 y Fo(\000)p Fr(1)2570 1110 y Fv(m)2655 1125 y Ft(I)2695 1110 y Fw(\()p Fv(U)g Fw(\))2890 1085 y(\025)2864 1110 y Fv(H)2970 1029 y Fp(\010)3028 1110 y Fv(m)3113 1125 y Ft(I)3153 1110 y Fw(\()p Fv(U)g Fw(\))p Fv(P)3368 1125 y Ft(I)3408 1029 y Fp(\011)3467 1051 y Fo(\000)p Fr(1)3561 999 y Fp(i)3608 1110 y Fv(:)35 1326 y Fw(Th)m(us)38 b Fv(D)390 1301 y Fw(~)370 1326 y Fv(Z)437 1341 y Ft(I)476 1326 y Fw(\()p Fv(H)8 b Fw(\))33 b(=)g Fv(X)897 1301 y Fw(\025)872 1326 y Fv(H)7 b(\016)1007 1290 y Fo(\000)p Fr(1)1101 1326 y Fw(,)37 b(where)g Fv(\016)g Fw(=)c Fv(m)1724 1341 y Ft(I)1765 1326 y Fw(\()p Fv(U)10 b Fw(\))p Fv(P)1980 1341 y Ft(I)2056 1326 y Fw(and)36 b Fv(X)41 b Fw(=)33 b Fv(m)2565 1341 y Ft(I)2601 1322 y Fe(c)2637 1326 y Fw(\()p Fv(U)10 b Fw(\))2789 1245 y Fp(\002)2831 1326 y Fv(I)2882 1290 y Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))3089 1326 y Fs(\000)25 b Fv(P)3254 1341 y Ft(I)3311 1326 y Fv(\016)3358 1290 y Fo(\000)p Fr(1)3469 1326 y Fv(m)3554 1341 y Ft(I)3594 1326 y Fw(\()p Fv(U)10 b Fw(\))3746 1245 y Fp(\003)3788 1326 y Fw(.)35 1465 y(Let)37 b Fv(X)295 1480 y Fr(1)370 1465 y Fw(b)s(e)f(the)g Fv(q)29 b Fs(\002)c Fv(q)39 b Fw(matrix)c(of)g(the)i Fv(q)i Fw(\014rst)e(columns)e(of)h Fv(X)8 b Fw(.)53 b(Then,)38 b Fv(X)2894 1440 y Fw(\025)2869 1465 y Fv(H)j Fw(=)33 b Fv(X)3181 1480 y Fr(1)3220 1465 y Fv(H)44 b Fw(and)36 b(w)m(e)h(get)35 1605 y Fv(D)140 1580 y Fw(~)119 1605 y Fv(Z)186 1620 y Ft(I)226 1605 y Fw(\()p Fv(H)8 b Fw(\))27 b(=)g Fv(X)602 1620 y Fr(1)642 1605 y Fv(H)8 b(\016)778 1569 y Fo(\000)p Fr(1)872 1605 y Fw(.)43 b(The)34 b(determinan)m(t)e(of)g(the)h(map)f(from)f Fv(M)2513 1620 y Ft(q)r(;p)2606 1605 y Fw(\()p Fq(C)37 b Fw(\))h(to)33 b Fv(M)3017 1620 y Ft(q)r(;p)3110 1605 y Fw(\()p Fq(C)k Fw(\))h(whic)m(h)33 b(sends)35 1744 y Fv(H)49 b Fw(to)40 b Fv(H)8 b(\016)428 1708 y Fo(\000)p Fr(1)562 1744 y Fw(is)40 b(\(det)17 b Fv(\016)t Fw(\))943 1708 y Fo(\000)p Ft(q)1036 1744 y Fw(.)68 b(The)41 b(determinan)m(t)g (of)f(the)h(map)f(from)f Fv(M)2750 1759 y Ft(q)r(;p)2844 1744 y Fw(\()p Fq(C)d Fw(\))47 b(to)40 b Fv(M)3270 1759 y Ft(q)r(;p)3363 1744 y Fw(\()p Fq(C)d Fw(\))46 b(whic)m(h)35 1884 y(sends)41 b Fv(H)47 b Fw(to)39 b Fv(X)638 1899 y Fr(1)678 1884 y Fv(H)46 b Fw(is)39 b(\(det)17 b Fv(X)1181 1899 y Fr(1)1221 1884 y Fw(\))1259 1848 y Ft(p)1298 1884 y Fw(,)41 b(so)f(det)17 b Fv(D)1749 1859 y Fw(~)1729 1884 y Fv(Z)1796 1899 y Ft(I)1874 1884 y Fw(=)39 b(\(det)17 b Fv(X)2260 1899 y Fr(1)2300 1884 y Fw(\))2338 1848 y Ft(p)2394 1884 y Fw(\(det)g Fv(\016)t Fw(\))2669 1848 y Fo(\000)p Ft(q)2762 1884 y Fw(.)63 b(W)-8 b(e)40 b(divide)f Fv(U)50 b Fw(in)m(to)38 b(four)35 2023 y(blo)s(c)m(ks:)135 2255 y Fv(U)h Fw(=)343 2084 y Fp( )491 2188 y Fv(U)557 2203 y Ft(q)706 2188 y Fv(U)772 2203 y Ft(q)r(;p)464 2328 y Fv(U)530 2343 y Ft(p;q)733 2328 y Fv(U)799 2343 y Ft(p)907 2084 y Fp(!)1003 2255 y Fv(;)114 b(U)1210 2270 y Ft(q)1276 2255 y Fs(2)28 b Fv(M)1464 2270 y Ft(q)1502 2255 y Fw(\()p Fq(C)37 b Fw(\))p Fv(;)55 b(U)1809 2270 y Ft(p)1877 2255 y Fs(2)28 b Fv(M)2065 2270 y Ft(p)2105 2255 y Fw(\()p Fq(C)37 b Fw(\))p Fv(;)54 b(U)2411 2270 y Ft(p;q)2532 2255 y Fs(2)29 b Fv(M)2721 2270 y Ft(p;q)2814 2255 y Fw(\()p Fq(C)37 b Fw(\))p Fv(;)55 b(U)3121 2270 y Ft(q)r(;p)3242 2255 y Fs(2)28 b Fv(M)3430 2270 y Ft(q)r(;p)3523 2255 y Fw(\()p Fq(C)37 b Fw(\))p Fv(:)35 2538 y Fw(Then)47 b Fv(\016)53 b Fw(=)d Fv(U)591 2553 y Ft(p;q)701 2538 y Fv(Z)768 2553 y Ft(I)838 2538 y Fw(+)31 b Fv(U)1011 2553 y Ft(p)1051 2538 y Fw(,)48 b(so)e Fv(X)1340 2553 y Fr(1)1429 2538 y Fw(=)j Fv(U)1620 2553 y Ft(q)1689 2538 y Fs(\000)1798 2457 y Fp(\000)1843 2538 y Fv(U)1909 2553 y Ft(q)1964 2538 y Fv(Z)2031 2553 y Ft(I)2102 2538 y Fw(+)30 b Fv(U)2274 2553 y Ft(q)r(;p)2368 2457 y Fp(\001)16 b(\000)2476 2538 y Fv(U)2542 2553 y Ft(p;q)2652 2538 y Fv(Z)2719 2553 y Ft(I)2789 2538 y Fw(+)31 b Fv(U)2962 2553 y Ft(p)3002 2457 y Fp(\001)3048 2479 y Fo(\000)p Fr(1)3159 2538 y Fv(U)3225 2553 y Ft(q)r(;p)3318 2538 y Fw(.)82 b(Let)45 b Fv(Z)53 b Fw(in)35 2677 y Fv(M)129 2692 y Ft(p)p Fr(+)p Ft(q)r(;p)p Fr(+)p Ft(q)402 2677 y Fw(\()p Fq(C)37 b Fw(\))46 b(b)s(e)c(the)f(matrix)e(with)i(blo)s(c)m (ks)g Fv(Z)1852 2692 y Ft(q)1932 2677 y Fw(=)g Fv(I)2100 2641 y Fr(\()p Ft(q)r Fr(\))2193 2677 y Fw(,)i Fv(Z)2330 2692 y Ft(p;q)2465 2677 y Fw(=)f(0,)h Fv(Z)2769 2692 y Ft(q)r(;p)2903 2677 y Fw(=)f Fv(Z)3088 2692 y Ft(I)3128 2677 y Fw(,)h Fv(Z)3265 2692 y Ft(p)3346 2677 y Fw(=)f Fv(I)3515 2641 y Fr(\()p Ft(p)p Fr(\))3609 2677 y Fw(,)h(the)35 2817 y(notations)i(b)s(eing)f(the)i(same)f(as)g(ab)s(o)m(v)m(e.)83 b(W)-8 b(riting)43 b(det)17 b Fv(U)60 b Fw(=)49 b(det)q(\()p Fv(U)10 b(Z)d Fw(\))45 b(and)g(using)g(the)h(column)35 2956 y(transformation)25 b Fv(C)764 2971 y Fr(1)831 2956 y Fs( )j Fv(C)1029 2971 y Fr(1)1079 2956 y Fs(\000)11 b Fv(C)1237 2971 y Fr(2)1294 2875 y Fp(\000)1339 2956 y Fv(U)1405 2971 y Ft(p;q)1515 2956 y Fv(Z)1582 2971 y Ft(I)1633 2956 y Fw(+)g Fv(U)1786 2971 y Ft(p)1826 2875 y Fp(\001)1872 2898 y Fo(\000)p Fr(1)1983 2956 y Fv(U)2049 2971 y Ft(p;q)2169 2956 y Fw(where)29 b Fv(C)2516 2971 y Fr(1)2582 2956 y Fw(is)e(made)g(of)f(the)i(\014rst)g Fv(q)j Fw(columns)35 3096 y(and)i Fv(C)295 3111 y Fr(2)367 3096 y Fw(of)f(the)h(remaining)d(ones,)k(w)m(e)f(get)341 3287 y(det)17 b Fv(U)38 b Fw(=)28 b(det)836 3176 y Fp(h)883 3287 y Fv(U)949 3302 y Ft(q)1010 3287 y Fs(\000)1109 3206 y Fp(\000)1155 3287 y Fv(U)1221 3302 y Ft(q)1276 3287 y Fv(Z)1343 3302 y Ft(I)1405 3287 y Fw(+)22 b Fv(U)1569 3302 y Ft(q)r(;p)1662 3206 y Fp(\001)16 b(\000)1770 3287 y Fv(U)1836 3302 y Ft(p;q)1946 3287 y Fv(Z)2013 3302 y Ft(I)2075 3287 y Fw(+)22 b Fv(U)2239 3302 y Ft(p)2279 3206 y Fp(\001)2324 3228 y Fo(\000)p Fr(1)2435 3287 y Fv(U)2501 3302 y Ft(p;q)2595 3176 y Fp(i)2664 3287 y Fs(\002)h Fw(det)2899 3206 y Fp(\000)2945 3287 y Fv(U)3011 3302 y Ft(p;q)3104 3287 y Fv(Z)3171 3302 y Ft(I)3233 3287 y Fw(+)f Fv(U)3397 3302 y Ft(p)3437 3206 y Fp(\001)3483 3287 y Fv(:)35 3517 y Fw(Hence)325 3432 y Fp(\014)325 3492 y(\014)359 3517 y Fw(det)33 b Fv(D)632 3492 y Fw(~)611 3517 y Fv(Z)678 3532 y Ft(I)718 3432 y Fp(\014)718 3492 y(\014)751 3458 y Fr(2)818 3517 y Fw(=)922 3432 y Fp(\014)922 3492 y(\014)955 3517 y Fw(det)17 b Fv(\016)1154 3432 y Fp(\014)1154 3492 y(\014)1187 3458 y Fo(\000)p Fr(2\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))1460 3517 y Fw(.)44 b(W)-8 b(e)33 b(ha)m(v)m(e)1946 3492 y(~)1924 3517 y Fv(P)1987 3532 y Ft(I)2054 3517 y Fw(=)28 b Fv(AP)2294 3532 y Ft(I)2334 3517 y Fv(\016)2381 3481 y Fo(\000)p Fr(1)2475 3517 y Fw(,)33 b(so)335 3720 y Fv(\025)396 3734 y Fd(e)392 3750 y Ft(I)460 3720 y Fw(=)27 b(det)699 3639 y Fp(\000)761 3679 y Ft(t)796 3695 y Fw(~)774 3720 y Fv(P)837 3735 y Ft(I)p 894 3617 60 4 v 899 3695 a Fw(~)877 3720 y Fv(P)953 3735 y Ft(I)993 3639 y Fp(\001)1039 3662 y Fo(\000)p Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))1305 3720 y Fw(=)h(det)1544 3639 y Fp(\000)1606 3679 y Ft(t)1619 3720 y Fv(P)1682 3735 y Ft(I)p 1739 3640 V 1722 3720 a Fv(P)1799 3735 y Ft(I)1838 3639 y Fp(\001)1884 3662 y Fo(\000)p Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2145 3720 y Fs(\002)2244 3635 y Fp(\014)2244 3695 y(\014)2277 3720 y Fw(det)17 b Fv(\016)2476 3635 y Fp(\014)2476 3695 y(\014)2521 3662 y Fr(2\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2768 3720 y Fw(=)27 b Fv(\025)2928 3735 y Ft(I)2985 3635 y Fp(\014)2985 3695 y(\014)3018 3720 y Fw(det)17 b Fv(D)3274 3695 y Fw(~)3254 3720 y Fv(Z)3321 3735 y Ft(I)3360 3635 y Fp(\014)3360 3695 y(\014)3394 3662 y Fo(\000)p Fr(2)3488 3720 y Fv(;)35 3908 y Fw(whic)m(h)34 b(pro)m(v)m(es)g(the)f(result.)p 3744 3908 4 66 v 3748 3846 59 4 v 3748 3908 V 3806 3908 4 66 v 35 4109 a Fi(Pr)n(oposition)38 b(2.3)p Fw(.)43 b(|)148 b(1.)41 b Fv(dV)1397 3998 y Fp(\020)1423 4109 y Fh(G)1541 4139 y Ft(p;q)1634 3998 y Fp(\021)1721 4109 y Fw(=)28 b Fv(\021)t Fu(.)135 4320 y Fw(2.)41 b Fu(If)35 b Fv(I)g Fs(2)28 b(I)7 b Fu(,)654 4205 y Fp(\014)654 4265 y(\014)654 4325 y(\014)654 4320 y Fh(G)771 4350 y Ft(p;q)864 4205 y Fp(\014)864 4265 y(\014)864 4325 y(\014)898 4389 y Ft(I)965 4320 y Fw(=)1069 4209 y Fp(n)1135 4320 y Fw(det)1271 4239 y Fp(\000)1316 4320 y Fv(I)1367 4284 y Fr(\()p Ft(p)p Fr(\))1484 4320 y Fw(+)1560 4284 y Ft(t)1595 4320 y Fv(Z)1662 4335 y Ft(I)p 1718 4240 58 4 v 1701 4320 a Fv(Z)1775 4335 y Ft(I)1815 4239 y Fp(\001)1861 4209 y(o)1927 4231 y Fo(\000)p Fr(\()p Ft(p)p Fr(+)p Ft(q)r Fr(\))2166 4320 y Fu(.)135 4512 y Fw(3.)41 b Fs(R)353 4401 y Fp(\020)380 4512 y Fh(G)497 4542 y Ft(p;q)590 4401 y Fp(\021)678 4512 y Fw(=)27 b(\()p Fv(p)22 b Fw(+)g Fv(q)t Fw(\))-33 b Fh(G)1157 4542 y Ft(p;q)1250 4512 y Fu(.)35 4727 y(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(1.)56 b(Let)37 b Fv(I)44 b Fw(in)36 b Fs(I)7 b Fw(.)56 b(It)37 b(is)f(easy)i(to)e(compute)t Fh(G)2170 4757 y Ft(p;q)2300 4727 y Fw(at)g(the)h(p)s(oin)m(t)f Fv(Z)2921 4742 y Ft(I)2996 4727 y Fw(=)e(0:)19 b Fh(G)3318 4757 y Ft(p;q)3412 4727 y Fw(\()p Fv(H)r(;)e(K)7 b Fw(\))34 b(=)35 4866 y Fv(T)14 b(r)s Fw(\()p Fv(H)p 296 4786 74 4 v 7 w(K)7 b Fw(\).)48 b(Then)35 b Fv(dV)21 b Fw(\()-33 b Fh(G)990 4897 y Ft(p;q)1083 4866 y Fw(\))1121 4832 y Fp(\014)1121 4892 y(\014)1154 4917 y Ft(Z)1202 4928 y Fe(I)1237 4917 y Fr(=0)1361 4866 y Fw(=)1467 4786 y Fp(\000)1513 4866 y Fv(i=)p Fw(2)1644 4786 y Fp(\001)1689 4808 y Ft(pq)1779 4786 y Fp(\000)1825 4866 y Fv(d)-5 b(Z)29 b Fs(^)24 b Fv(d)p 2125 4786 58 4 v(Z)2181 4786 y Fp(\001)2227 4905 y Ft(I)2297 4866 y Fw(=)29 b Fv(\021)2450 4832 y Fp(\014)2450 4892 y(\014)2484 4917 y Ft(Z)2532 4928 y Fe(I)2567 4917 y Fr(=0)2661 4866 y Fw(.)47 b(Since)34 b Fv(dV)22 b Fw(\()-33 b Fh(G)3244 4897 y Ft(p;q)3337 4866 y Fw(\))33 b(and)h Fv(\021)k Fw(are)35 5044 y(in)m(v)-5 b(arian)m(t)32 b(b)m(y)h(the)g(transitiv)m (e)f(action)g(of)g Fv(U)10 b Fw(\()p Fv(p)23 b Fw(+)f Fv(q)t Fw(\),)32 b(w)m(e)i(ha)m(v)m(e)g Fv(dV)21 b Fw(\()-33 b Fh(G)2635 5074 y Ft(p;q)2728 5044 y Fw(\))27 b(=)h Fv(\021)t Fw(.)35 5232 y(2.)44 b(Since)32 b Fv(dV)22 b Fw(\()-33 b Fh(G)661 5263 y Ft(p;q)755 5232 y Fw(\))27 b(=)924 5148 y Fp(\014)924 5207 y(\014)924 5232 y Fh(G)1042 5263 y Ft(p;q)1135 5148 y Fp(\014)1135 5207 y(\014)1168 5271 y Ft(I)1225 5232 y Fw(\()p Fv(i=)p Fw(2\))1432 5196 y Ft(pq)1522 5152 y Fp(\000)1567 5232 y Fv(d)-5 b(Z)29 b Fs(^)22 b Fv(d)p 1865 5152 V(Z)1922 5152 y Fp(\001)1967 5271 y Ft(I)2007 5232 y Fw(,)33 b(prop)s(ert)m(y)g(1)g(giv)m(es)g(the)g (result.)p eop %%Page: 6 6 6 5 bop 35 283 a Fk(6)1490 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 634 y Fw(3.)54 b(Remark)35 b(that)s Fh(G)835 665 y Ft(p;q)961 634 y Fw(=)e Fv(i)17 b(@)p 1176 553 57 4 v 5 w(@)40 b Fw(log)1393 554 y Fp(\010)1451 634 y Fw(det)q(\()p Fv(I)1676 598 y Fr(\()p Ft(p)p Fr(\))1794 634 y Fw(+)1870 598 y Ft(t)1891 634 y Fv(Z)1958 649 y Ft(I)p 2014 554 58 4 v 1997 634 a Fv(Z)2072 649 y Ft(I)2112 634 y Fw(\))2150 554 y Fp(\011)2208 634 y Fw(.)53 b(Since)36 b Fs(R)2647 524 y Fp(\020)2674 634 y Fh(G)2791 665 y Ft(p;q)2885 524 y Fp(\021)2977 634 y Fw(=)d Fs(\000)p Fv(i)17 b(@)p 3269 553 57 4 v 5 w(@)41 b Fw(log)3503 520 y Fp(\014)3503 579 y(\014)3503 639 y(\014)3504 634 y Fh(G)3622 665 y Ft(p;q)3715 520 y Fp(\014)3715 579 y(\014)3715 639 y(\014)3748 703 y Ft(I)3788 634 y Fw(,)35 826 y(w)m(e)46 b(obtain)d Fs(R)607 715 y Fp(\020)634 826 y Fh(G)751 856 y Ft(p;q)844 715 y Fp(\021)951 826 y Fw(=)k(\()p Fv(p)30 b Fw(+)g Fv(q)t Fw(\))-33 b Fh(G)1466 856 y Ft(p;q)1560 826 y Fw(,)47 b(whic)m(h)d(expresses)j(that)12 b Fh(G)2665 856 y Ft(p;q)2802 826 y Fw(is)44 b(Einstein,)j(with)c(factor)35 966 y Fv(p)23 b Fw(+)f Fv(q)t Fw(.)p 3744 966 4 66 v 3748 903 59 4 v 3748 966 V 3806 966 4 66 v 784 1279 a Fx(3.)56 b(Some)38 b(general)f(results)g(ab)s(out)h(Tian's)f(in)m(v)-6 b(arian)m(t)35 1477 y(3.1.)57 b(Tian's)35 b(in)m(v)-6 b(arian)m(t)33 b(with)h(a)i(normalization)c(on)j(a)g(\014nite)g(set.)44 b(|)56 b Fw(If)31 b Fv(X)38 b Fw(is)30 b(a)g(manifold,)35 1616 y(w)m(e)k(will)c(denote)k(b)m(y)f Fv(\026)872 1631 y Ft(X)972 1616 y Fw(a)f(measure)h(on)f Fv(X)41 b Fw(compatible)30 b(with)i(the)h(manifold)d(structure.)35 1814 y Fi(Theorem)38 b(3.1)p Fw(.)43 b(|)49 b Fu(L)-5 b(et)41 b Fv(M)51 b Fu(b)-5 b(e)41 b(a)f(c)-5 b(omp)g(act)40 b(K\177)-50 b(ahler)40 b(manifold.)61 b(We)41 b(supp)-5 b(ose)40 b(that)i(ther)-5 b(e)40 b(exists)35 1953 y(a)45 b(c)-5 b(omp)g(act)44 b(Lie)h(gr)-5 b(oup)45 b Fv(G)g Fu(of)g(holomorphic)e (isometries.)74 b(L)-5 b(et)46 b Fw(\001)2583 1968 y Ft(n)2676 1953 y Fw(=)h Fs(f)p Fv(P)2912 1968 y Fr(1)2951 1953 y Fv(;)17 b(:)g(:)g(:)e(;)i(P)3232 1968 y Ft(n)3279 1953 y Fs(g)45 b Fu(b)-5 b(e)44 b(a)h(\014nite)35 2093 y(subset)d(of)g Fv(M)10 b Fu(.)66 b(L)-5 b(et)42 b Fv(\013)q Fw(\()p Fv(!)t Fw(\))e Fu(\(r)-5 b(esp.)65 b Fv(\013)1440 2119 y Fg(\001)1490 2127 y Fe(n)1540 2093 y Fw(\()p Fv(!)t Fw(\))41 b Fu(\))h(b)-5 b(e)41 b(the)h(supr)-5 b(emum)41 b(of)h(the)f(set)h(of)g(the)f(nonne)-5 b(gative)35 2232 y(r)g(e)g(al)32 b(numb)-5 b(ers)32 b Fv(\013)h Fu(satisfying)f(the)g(c) -5 b(ondition:)43 b(ther)-5 b(e)32 b(exists)g(a)g(c)-5 b(onstant)32 b Fv(C)39 b Fu(such)32 b(that)h(the)f(ine)-5 b(quality)35 2260 y Fp(Z)91 2486 y Ft(M)186 2396 y Fv(e)231 2355 y Fo(\000)p Ft(\013')435 2396 y Fs(\024)53 b Fv(C)i Fu(holds)48 b(for)g(al)5 b(l)48 b(the)g Fv(!)t Fu(-admissible)e (functions)i Fv(')g Fu(with)g Fw(sup)18 b Fv(')52 b Fs(\025)h Fw(0)c Fu(\(r)-5 b(esp.)84 b(with)35 2569 y Fv(')p Fw(\()p Fv(P)200 2584 y Ft(i)228 2569 y Fw(\))30 b Fs(\025)g Fw(0)36 b Fu(for)g Fw(1)29 b Fs(\024)h Fv(i)g Fs(\024)g Fv(n)p Fu(\).)48 b(Supp)-5 b(ose)36 b(in)f(addition)g(that)i(the)f (orbit)g(of)f(e)-5 b(ach)36 b Fv(P)3048 2584 y Ft(i)3112 2569 y Fu(under)f(the)h(action)35 2708 y(of)f Fv(G)g Fu(has)f(p)-5 b(ositive)34 b(me)-5 b(asur)g(e.)45 b(Then)34 b Fv(\013)q Fw(\()p Fv(!)t Fw(\))26 b(=)i Fv(\013)1855 2734 y Fg(\001)1905 2742 y Fe(n)1955 2708 y Fw(\()p Fv(!)t Fw(\))p Fu(.)35 2906 y Fw(W)-8 b(e)33 b(\014rst)g(establish)g(a)f(few)h (lemmas)e(whic)m(h)i(will)d(b)s(e)j(useful)g(for)f(the)h(pro)s(of.)35 3103 y Fi(Lemma)39 b(3.2)p Fw(.)k(|)48 b Fu(L)-5 b(et)928 3023 y Fp(\000)973 3103 y Fv(')1037 3118 y Ft(n)1084 3023 y Fp(\001)1130 3142 y Ft(n)p Fo(\025)p Fr(0)1296 3103 y Fu(b)g(e)29 b(a)g(se)-5 b(quenc)g(e)29 b(of)g(admissible)f (functions)h(with)g(nonne)-5 b(gative)28 b(max-)35 3243 y(ima.)55 b(Then)37 b(ther)-5 b(e)38 b(exists)g(a)g(subset)g Fw(\012)h Fu(of)f Fv(M)10 b Fu(,)40 b(with)e Fv(\026)2108 3269 y Fe(M)2179 3243 y Fw(\(\012\))c(=)g Fv(\026)2528 3269 y Fe(M)2599 3243 y Fw(\()p Fv(M)10 b Fw(\))p Fu(,)40 b(and)e(a)g(subse)-5 b(quenc)g(e)37 b Fv(')3730 3258 y Ft(n)3773 3270 y Fe(k)35 3382 y Fu(of)e Fv(')214 3397 y Ft(n)261 3382 y Fu(,)g(such)f(that)i(for)e(every)h Fv(!)j Fu(in)d Fw(\012)p Fu(,)1514 3302 y Fp(\000)1560 3382 y Fv(')1624 3397 y Ft(n)1667 3409 y Fe(k)1709 3382 y Fw(\()p Fv(!)t Fw(\))1850 3302 y Fp(\001)1894 3421 y Ft(k)r Fo(\025)p Fr(0)2062 3382 y Fu(is)g(b)-5 b(ounde)g(d)34 b(fr)-5 b(om)34 b(b)-5 b(elow.)35 3580 y(Pr)g(o)g(of)p Fw(.)43 b(|)e(Let)32 b Fv(Q)722 3595 y Ft(n)800 3580 y Fw(b)s(e)g(a)f(p)s(oin)m(t)f(suc)m(h)j(that)e Fv(')1758 3595 y Ft(n)1805 3580 y Fw(\()p Fv(Q)1920 3595 y Ft(n)1967 3580 y Fw(\))g(v)-5 b(anishes.)44 b(Green's)32 b(form)m(ula)e(runs)i (as)f(follo)m(ws:)840 3798 y Fv(')904 3813 y Ft(n)951 3798 y Fw(\()p Fv(Q)1066 3813 y Ft(n)1113 3798 y Fw(\))d(=)1307 3730 y(1)p 1293 3775 79 4 v 1293 3866 a Fv(V)1398 3662 y Fp(Z)1453 3887 y Ft(M)1549 3798 y Fv(')1613 3813 y Ft(n)1682 3798 y Fw(+)1780 3662 y Fp(Z)1835 3887 y Ft(M)1931 3798 y Fv(G)p Fw(\()p Fv(Q)2123 3813 y Ft(n)2170 3798 y Fv(;)17 b(R)q Fw(\))g(\001)p Fv(')2489 3813 y Ft(n)2535 3798 y Fw(\()p Fv(R)q Fw(\))g Fv(dV)k Fw(\()p Fv(R)q Fw(\))p Fv(;)35 4080 y Fw(with)37 b Fv(G)p Fw(\()p Fv(Q;)17 b(R)q Fw(\))34 b Fs(\024)h Fw(0)i(and)1036 3945 y Fp(Z)1092 4170 y Ft(M)1187 4080 y Fv(G)p Fw(\()p Fv(Q;)17 b(R)q Fw(\))g Fv(dV)k Fw(\()p Fv(R)q Fw(\))35 b(=)f Fs(\000)p Fv(C)7 b Fw(,)38 b(where)g Fv(C)44 b Fw(is)36 b(a)g(p)s(ositiv)m(e)g (constan)m(t.)57 b(Since)35 4314 y Fv(')99 4329 y Ft(n)177 4314 y Fw(is)30 b(admissible,)e(\001)p Fv(')915 4329 y Ft(n)993 4314 y Fw(is)i(greater)g(than)h Fs(\000)p Fv(m)p Fw(,)g Fv(m)g Fw(b)s(eing)f(the)g(dimension)f(of)h Fv(M)10 b Fw(.)44 b(Th)m(us)3393 4178 y Fp(Z)3448 4404 y Ft(M)3544 4314 y Fs(j)p Fv(')3636 4329 y Ft(n)3682 4314 y Fs(j)27 b(\024)35 4497 y Fv(C)d(m)17 b(V)k Fw(.)54 b(The)37 b(sequence)1002 4416 y Fp(\000)1048 4497 y Fv(')1112 4512 y Ft(n)1159 4416 y Fp(\001)1204 4536 y Ft(n)p Fo(\025)p Fr(0)1378 4497 y Fw(is)e(b)s(ounded)i(in)e Fv(L)2064 4461 y Fr(1)2104 4497 y Fw(\()p Fv(M)10 b Fw(\).)55 b(W)-8 b(e)36 b(can)g(therefore)h(extract)g(a)f(subse-)35 4640 y(quence)359 4559 y Fp(\000)404 4640 y Fv(')468 4655 y Ft(n)511 4667 y Fe(k)553 4559 y Fp(\001)599 4679 y Ft(n)642 4691 y Fe(k)680 4679 y Fo(2)p Ft(I)800 4640 y Fw(whic)m(h)e(con)m(v)m(erges)i(almost)c(ev)m(erywhere)k(to)e(a)f (function)g Fv(')g Fw(of)g Fv(L)3202 4604 y Fr(1)3242 4640 y Fw(\()p Fv(M)10 b Fw(\).)46 b(Since)34 b Fv(')35 4780 y Fw(is)f(\014nite)f(almost)f(ev)m(erywhere,)36 b(w)m(e)d(get)g(the)g(result.)p 3744 4780 4 66 v 3748 4717 59 4 v 3748 4780 V 3806 4780 4 66 v 35 4977 a Fi(Lemma)39 b(3.3)p Fw(.)k(|)48 b Fu(L)-5 b(et)928 4897 y Fp(\000)973 4977 y Fv(')1037 4992 y Ft(n)1084 4897 y Fp(\001)1130 5016 y Ft(n)p Fo(\025)p Fr(0)1296 4977 y Fu(b)g(e)29 b(a)g(se)-5 b(quenc)g(e)29 b(of)g(admissible)f(functions)h(with)g (nonne)-5 b(gative)28 b(max-)35 5117 y(ima)h(and)g(supp)-5 b(ose)28 b(that)i(ther)-5 b(e)29 b(exists)f(a)h(c)-5 b(omp)g(act)29 b(gr)-5 b(oup)29 b Fv(G)g Fu(of)g(holomorphic)e (isometries)h(of)h Fv(M)40 b Fu(such)35 5256 y(that)33 b(the)f(orbit)f(of)h(e)-5 b(ach)31 b Fv(P)1011 5271 y Ft(i)1071 5256 y Fu(has)g(p)-5 b(ositive)31 b(me)-5 b(asur)g(e.)44 b(L)-5 b(et)32 b Fw(\010)c(:)g Fv(G)f Fs(!)h Fq(R)20 b Fs([)c(f\0001g)37 b Fu(b)-5 b(e)32 b(the)g(map)f(de\014ne)-5 b(d)35 5396 y(by)35 b Fw(\010\()p Fv(g)t Fw(\))28 b(=)f(inf)499 5458 y Fr(\001)558 5466 y Fe(n)630 5396 y Fw(inf)625 5458 y Ft(k)r Fo(\025)p Fr(0)754 5396 y Fw(\()p Fv(')856 5411 y Ft(k)920 5396 y Fs(\016)22 b Fv(g)t Fw(\))p Fu(.)44 b(Then)34 b(ther)-5 b(e)35 b(exists)g Fv(g)j Fu(in)c Fv(G)h Fu(such)g(that)g Fw(\010\()p Fv(g)t Fw(\))f Fu(is)h(\014nite.)p eop %%Page: 7 7 7 6 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h (GRASSMANN)d(MANIF)n(OLD)804 b Fk(7)35 619 y Fu(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(Supp)s(ose)c(that)e(\010)f Fs(\021)f(\0001)p Fw(.)53 b(F)-8 b(or)35 b Fv(i)e Fw(=)g(1)p Fv(;)17 b(:)g(:)g(:)e(;)i(n) p Fw(,)37 b(let)e Fv(A)2501 634 y Ft(i)2565 619 y Fw(b)s(e)g(the)i(set) f(of)f(the)h Fv(g)j Fw(in)c Fv(G)g Fw(suc)m(h)35 759 y(that)k(inf)248 822 y Ft(k)r Fo(\025)p Fr(0)376 759 y Fw(\()p Fv(')478 774 y Ft(k)544 759 y Fs(\016)22 b Fv(g)t Fw(\)\()p Fv(P)806 774 y Ft(i)833 759 y Fw(\))30 b(=)f Fs(\0001)p Fw(.)46 b(The)35 b(sets)f Fv(A)1722 774 y Ft(i)1784 759 y Fw(are)g(measurable)e(and)i Fs([)2715 718 y Ft(n)2715 783 y(i)p Fr(=1)2834 759 y Fv(A)2907 774 y Ft(i)2964 759 y Fw(=)29 b Fv(G)p Fw(,)34 b(so)g(there)g(exists)35 926 y Fv(i)f Fw(suc)m(h)g(that)e Fv(A)603 941 y Ft(i)664 926 y Fw(has)h(p)s(ositiv)m(e)f(measure.)44 b(F)-8 b(rom)30 b(Lemma)g(\(3.2\),)i Fv(A)2550 941 y Ft(i)2578 926 y Fv(:P)2668 941 y Ft(i)2728 926 y Fw(is)g(a)f(subset)j(of)d(\012)3385 890 y Ft(c)3420 926 y Fw(.)44 b(Since)32 b(\012)35 1065 y(and)f Fv(M)40 b Fw(ha)m(v)m(e)32 b(the)e(same)g(measure,)h(the)g (measure)f(of)g Fv(A)2117 1080 y Ft(i)2145 1065 y Fv(:P)2235 1080 y Ft(i)2294 1065 y Fw(v)-5 b(anishes.)43 b(Let)30 b Fv(u)2942 1080 y Ft(i)3000 1065 y Fw(b)s(e)g(the)h(map)e(from)g Fv(G)35 1205 y Fw(to)f Fv(M)39 b Fw(whic)m(h)28 b(sends)i Fv(g)h Fw(to)d Fv(g)t Fw(\()p Fv(P)1159 1220 y Ft(i)1186 1205 y Fw(\).)42 b(Then)29 b Fv(u)1599 1220 y Ft(i)1655 1205 y Fw(has)f(constan)m(t)h(rank)f(on)g Fv(G)p Fw(.)42 b(Indeed,)30 b Fv(u)3106 1220 y Ft(i)3147 1205 y Fs(\016)13 b Fv(L)p Fw(\()p Fv(g)t Fw(\))27 b(=)g Fv(\033)3588 1220 y Ft(g)3642 1205 y Fs(\016)13 b Fv(u)3761 1220 y Ft(i)3788 1205 y Fw(,)35 1344 y(where)39 b Fv(L)p Fw(\()p Fv(g)t Fw(\))d(is)g(the)i(left)e(translation)f(b)m(y)j Fv(g)i Fw(and)d Fv(\033)1975 1359 y Ft(g)2052 1344 y Fw(the)g(map)g(from)e Fv(M)48 b Fw(to)36 b Fv(M)48 b Fw(whic)m(h)37 b(sends)i Fv(x)e Fw(to)35 1484 y Fv(g)t(:x)p Fw(.)43 b(Since)29 b Fv(G:P)656 1499 y Ft(i)713 1484 y Fw(has)g(p)s(ositiv)m(e)g(measure,) h Fv(u)1701 1499 y Ft(i)1757 1484 y Fw(is)f(a)g(submersion)g(on)g Fv(G)p Fw(,)g(so)g(that)g Fv(u)3082 1499 y Ft(i)3110 1484 y Fw(\()p Fv(A)3221 1499 y Ft(i)3249 1484 y Fw(\))g(has)h(p)s (ositiv)m(e)35 1623 y(measure.)44 b(This)33 b(is)f(a)g(con)m (tradiction)g(since)h Fv(u)1744 1638 y Ft(i)1772 1623 y Fw(\()p Fv(A)1883 1638 y Ft(i)1911 1623 y Fw(\))27 b(=)h Fv(A)2153 1638 y Ft(i)2181 1623 y Fv(:P)2271 1638 y Ft(i)2299 1623 y Fw(.)p 3744 1623 4 66 v 3748 1561 59 4 v 3748 1623 V 3806 1623 4 66 v 35 1812 a(W)-8 b(e)33 b(can)g(no)m(w)g(pro)m(v)m(e)h(Theorem)f(\(3.1\).)35 2002 y Fu(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(It)34 b(is)g(clear)f(that)h Fv(\013)q Fw(\()p Fv(!)t Fw(\))29 b Fs(\024)i Fv(\013)1528 2028 y Fg(\001)1578 2036 y Fe(n)1629 2002 y Fw(\()p Fv(!)t Fw(\).)47 b(Con)m(v)m(ersely)-8 b(,)36 b(let)e Fv(")c(>)g Fw(0.)47 b(There)36 b(exists)e(a)g(sequence)35 2099 y Fp(\000)81 2180 y Fv(')145 2195 y Ft(n)192 2099 y Fp(\001)238 2219 y Ft(n)p Fo(\025)p Fr(0)412 2180 y Fw(of)k(admissible)d(functions) j(with)f(p)s(ositiv)m(e)g(maxima)e(suc)m(h)k(that)2843 2044 y Fp(Z)2898 2270 y Ft(M)2994 2180 y Fv(e)3039 2139 y Fo(\000)p Fr(\()p Ft(\013)p Fr(\()p Ft(!)r Fr(\)+)p Ft(")p Fr(\))p Ft(')3427 2151 y Fe(k)3509 2180 y Fw(go)s(es)e(to)35 2347 y(in\014nit)m(y)31 b(as)g Fv(k)k Fw(go)s(es)c(to)g(in\014nit)m(y) -8 b(.)42 b(Replacing)30 b Fv(')1784 2362 y Ft(n)1862 2347 y Fw(b)m(y)i Fv(')2060 2362 y Ft(n)2126 2347 y Fs(\000)20 b Fw(sup)d Fv(')2450 2362 y Ft(n)2497 2347 y Fw(,)32 b(w)m(e)g(can)g(tak)m(e)g(sup)17 b Fv(')3313 2362 y Ft(n)3388 2347 y Fw(=)27 b(0.)43 b(First)35 2487 y(w)m(e)34 b(apply)f (Lemma\(3.2\).)43 b(F)-8 b(or)32 b(the)h(sak)m(e)h(of)f(simplicit)m(y) -8 b(,)30 b(w)m(e)k(tak)m(e)g Fv(')2587 2502 y Ft(n)2630 2514 y Fe(k)2700 2487 y Fw(=)28 b Fv(')2868 2502 y Ft(k)2911 2487 y Fw(.)44 b(F)-8 b(rom)32 b(Lemma)f(\(3.3\),)35 2626 y(there)d(exists)g(an)f(elemen)m(t)f Fv(g)31 b Fw(in)26 b Fv(G)h Fw(suc)m(h)h(that)f(\010\()p Fv(g)t Fw(\))f(is)h(\014nite;)h (w)m(e)g(de\014ne)h(\011)2816 2641 y Ft(k)2885 2626 y Fw(b)m(y)f(\011)3091 2641 y Ft(k)3161 2626 y Fw(=)g Fv(')3329 2641 y Ft(k)3382 2626 y Fs(\016)11 b Fv(g)j Fs(\000)d Fw(\010\()p Fv(g)t Fw(\).)35 2766 y(Since)38 b Fv(g)j Fw(is)c(an)h(isometry)-8 b(,)38 b(\011)1127 2781 y Ft(k)1207 2766 y Fw(is)f Fv(!)t Fw(-admissible,)f(and)i(from)e(the)i(v)m(ery)h (de\014nition)e(of)g(\010,)i(\011)3502 2781 y Ft(k)3545 2766 y Fw(\()p Fv(P)3646 2781 y Ft(i)3674 2766 y Fw(\))e(is)35 2935 y(nonnegativ)m(e.)84 b(F)-8 b(urthermore,)1263 2799 y Fp(Z)1318 3025 y Ft(M)1414 2935 y Fv(e)1459 2894 y Fo(\000)p Fr(\()p Ft(\013)p Fr(\()p Ft(!)r Fr(\)+)p Ft(")p Fr(\)\011)1856 2906 y Fe(k)1950 2935 y Fw(=)50 b Fv(e)2121 2894 y Fr(\()p Ft(\013)p Fr(\()p Ft(!)r Fr(\)+)p Ft(")p Fr(\)\010\()p Ft(g)r Fr(\))2572 2799 y Fp(Z)2628 3025 y Ft(M)2723 2935 y Fv(e)2768 2894 y Fo(\000)p Fr(\()p Ft(\013)p Fr(\()p Ft(!)r Fr(\)+)p Ft(")p Fr(\))p Ft(')3156 2906 y Fe(k)3201 2935 y Fw(.)82 b(This)46 b(pro)m(v)m(es)35 3168 y(that)245 3033 y Fp(Z)300 3258 y Ft(M)396 3168 y Fv(e)441 3127 y Fo(\000)p Fr(\()p Ft(\013)p Fr(\()p Ft(!)r Fr(\)+)p Ft(")p Fr(\)\011)838 3139 y Fe(k)913 3168 y Fw(go)s(es)31 b(to)g(in\014nit)m(y)f(as)h Fv(k)j Fw(go)s(es)d(to)f(in\014nit)m(y)-8 b(.)43 b(Then,)32 b Fv(\013)2819 3195 y Fg(\001)2869 3203 y Fe(n)2920 3168 y Fw(\()p Fv(!)t Fw(\))27 b Fs(\024)h Fv(\013)q Fw(\()p Fv(!)t Fw(\))18 b(+)g Fv(")p Fw(.)43 b(This)35 3341 y(inequalit)m(y)32 b(holds)g(for)g(ev)m(ery)j(p)s(ositiv)m(e)d Fv(")p Fw(,)g(and)h(so)f Fv(\013)1987 3368 y Fg(\001)2037 3376 y Fe(n)2088 3341 y Fw(\()p Fv(!)t Fw(\))27 b Fs(\024)h Fv(\013)q Fw(\()p Fv(!)t Fw(\).)p 3744 3341 V 3748 3279 59 4 v 3748 3341 V 3806 3341 4 66 v 35 3562 a Fx(3.2.)57 b(Tian's)43 b(in)m(v)-6 b(arian)m(t)41 b(on)j(a)f(pro)s(duct.)h(|)65 b Fw(F)-8 b(or)36 b(a)h(K\177)-49 b(ahler)37 b(form)f Fv(!)41 b Fw(on)c(a)g(compact)g(K\177)-49 b(ahler)35 3702 y(manifold)30 b Fv(M)10 b Fw(,)34 b Fv(\013)q Fw(\()p Fv(!)t Fw(\))d(is)h(de\014ned)i (as)f(in)f(Theorem)h(\(3.1\).)35 3899 y Fi(Pr)n(oposition)38 b(3.4)p Fw(.)43 b(|)48 b Fu(L)-5 b(et)1219 3819 y Fp(\000)1264 3899 y Fv(M)1358 3914 y Ft(i)1387 3819 y Fp(\001)1433 3938 y Fr(1)p Fo(\024)p Ft(i)p Fo(\024)p Ft(n)1700 3899 y Fu(b)g(e)50 b(c)-5 b(omp)g(act)50 b(K\177)-50 b(ahler)51 b(manifolds)e(with)i(metric)g(forms)35 3962 y Fp(\000)81 4043 y Fv(!)142 4058 y Ft(i)170 3962 y Fp(\001)216 4082 y Fr(1)p Fo(\024)p Ft(i)p Fo(\024)p Ft(n)432 4043 y Fu(.)61 b(We)41 b(endow)f(the)g(pr)-5 b(o)g(duct)41 b Fv(M)1623 4058 y Fr(1)1689 4043 y Fs(\002)27 b(\001)17 b(\001)g(\001)25 b(\002)h Fv(M)2133 4058 y Ft(n)2221 4043 y Fu(with)41 b(the)f(metric)h Fv(!)2981 4058 y Fr(1)3046 4043 y Fs(\010)27 b(\001)17 b(\001)g(\001)24 b(\010)j Fv(!)3457 4058 y Ft(n)3504 4043 y Fu(.)62 b(Then)35 4182 y Fv(\013)q Fw(\()p Fv(!)197 4197 y Fr(1)258 4182 y Fs(\010)23 b(\001)17 b(\001)g(\001)j(\010)j Fv(!)657 4197 y Ft(n)704 4182 y Fw(\))k(=)75 b(inf)873 4243 y Fr(1)p Fo(\024)p Ft(i)p Fo(\024)p Ft(n)1101 4182 y Fv(\013)q Fw(\()p Fv(!)1263 4197 y Ft(i)1291 4182 y Fw(\))p Fu(.)35 4400 y(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(It)46 b(su\016ces)h(to)e(mak)m(e)h(the)f(pro)s (of)g(when)h Fv(n)k Fw(=)f(2,)g(the)c(general)g(result)g(will)e(follo)m (w)h(b)m(y)35 4539 y(induction.)35 4728 y(\(1\))36 b(Supp)s(ose)h(that) f Fv(\013)q Fw(\()p Fv(!)959 4743 y Fr(1)998 4728 y Fw(\))e Fs(\024)g Fv(\013)q Fw(\()p Fv(!)1343 4743 y Fr(2)1382 4728 y Fw(\),)j(and)f(let)g Fv(")d(>)h Fw(0.)54 b(There)37 b(exists)g(a)f(sequence)3192 4647 y Fp(\000)3238 4728 y Fv(')3302 4743 y Ft(n)3349 4647 y Fp(\001)3394 4767 y Ft(n)p Fo(\025)p Fr(0)3568 4728 y Fw(of)f Fv(!)3743 4743 y Fr(1)3782 4728 y Fw(-)35 4922 y(admissible)30 b(functions)i(on)g Fv(M)1156 4937 y Fr(1)1227 4922 y Fw(with)f(p)s(ositiv)m(e)h(maxima)d(suc)m(h)k(that)2609 4786 y Fp(Z)2664 5012 y Ft(M)2732 5021 y Fg(1)2787 4922 y Fv(e)2832 4876 y Fo(\000)2887 4795 y Fp(\000)2933 4876 y Ft(\013)p Fr(\()p Ft(!)3049 4885 y Fg(1)3084 4876 y Fr(\)+)p Ft(")3199 4795 y Fp(\001)3245 4876 y Ft(')3291 4884 y Fe(n)3369 4922 y Fw(go)s(es)f(to)f(in-)35 5104 y(\014nit)m(y)24 b(when)g Fv(n)g Fw(go)s(es)f(to)g(in\014nit)m(y)-8 b(.)40 b(W)-8 b(e)23 b(de\014ne)i Fv( )1780 5119 y Ft(n)1850 5104 y Fw(on)e Fv(M)2070 5119 y Fr(1)2113 5104 y Fs(\002)s Fv(M)2287 5119 y Fr(2)2351 5104 y Fw(b)m(y)h Fv( )2540 5119 y Ft(n)2588 5104 y Fw(\()p Fv(m)2711 5119 y Fr(1)2750 5104 y Fv(;)17 b(m)2879 5119 y Fr(2)2919 5104 y Fw(\))27 b(=)h Fv(')3152 5119 y Ft(n)3199 5104 y Fw(\()p Fv(m)3322 5119 y Fr(1)3361 5104 y Fw(\).)41 b(Th)m(us)25 b Fv( )3768 5119 y Ft(n)35 5273 y Fw(is)k(\()p Fv(!)229 5288 y Fr(1)284 5273 y Fs(\010)16 b Fv(!)438 5288 y Fr(2)477 5273 y Fw(\)-admissible)27 b(on)i Fv(M)1243 5288 y Fr(1)1299 5273 y Fs(\002)16 b Fv(M)1486 5288 y Fr(2)1525 5273 y Fw(,)30 b(with)f(p)s(ositiv)m(e)g (maxim)m(um,)f(and)2825 5137 y Fp(Z)2881 5363 y Ft(M)2949 5372 y Fg(1)2983 5363 y Fo(\002)p Ft(M)3106 5372 y Fg(2)3161 5273 y Fv(e)3206 5227 y Fo(\000)3261 5146 y Fp(\000)3307 5227 y Ft(\013)p Fr(\()p Ft(!)3423 5236 y Fg(1)3458 5227 y Fr(\)+)p Ft(")3573 5146 y Fp(\001)3619 5227 y Ft( )3665 5235 y Fe(n)3739 5273 y Fw(=)p eop %%Page: 8 8 8 7 bop 35 283 a Fk(8)1490 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 655 y Fv(V)22 b Fw(\()p Fv(M)246 670 y Fr(2)286 655 y Fw(\))341 520 y Fp(Z)396 745 y Ft(M)464 754 y Fg(1)519 655 y Fv(e)564 610 y Fo(\000)619 529 y Fp(\000)664 610 y Ft(\013)p Fr(\()p Ft(!)780 619 y Fg(1)816 610 y Fr(\)+)p Ft(")931 529 y Fp(\001)976 610 y Ft(')1022 618 y Fe(n)1069 655 y Fw(,)47 b(so)e(that)1498 520 y Fp(Z)1553 745 y Ft(M)1621 754 y Fg(1)1655 745 y Fo(\002)p Ft(M)1778 754 y Fg(2)1833 655 y Fv(e)1878 610 y Fo(\000)1933 529 y Fp(\000)1979 610 y Ft(\013)p Fr(\()p Ft(!)2095 619 y Fg(1)2130 610 y Fr(\)+)p Ft(")2245 529 y Fp(\001)2291 610 y Ft( )2337 618 y Fe(n)2428 655 y Fw(go)s(es)f(to)g(in\014nit)m(y)g (when)h Fv(n)g Fw(go)s(es)f(to)35 837 y(in\014nit)m(y)-8 b(.)43 b(W)-8 b(e)33 b(ha)m(v)m(e)h(therefore)f Fv(\013)q Fw(\()p Fv(!)1365 852 y Fr(1)1426 837 y Fs(\010)23 b Fv(!)1587 852 y Fr(2)1626 837 y Fw(\))28 b Fs(\024)g Fv(\013)q Fw(\()p Fv(!)1959 852 y Fr(1)1998 837 y Fw(\))22 b(+)g Fv(")p Fw(.)43 b(This)33 b(yields)f Fv(\013)q Fw(\()p Fv(!)2931 852 y Fr(1)2992 837 y Fs(\010)22 b Fv(!)3152 852 y Fr(2)3191 837 y Fw(\))28 b Fs(\024)g Fv(\013)q Fw(\()p Fv(!)3524 852 y Fr(1)3563 837 y Fw(\).)35 1026 y(\(2\))42 b(Let)h(us)g(no)m(w)g(pro)m(v)m(e)g(the)g(opp)s(osite)f (inequalit)m(y)-8 b(.)71 b(Let)43 b Fv(\013)g Fw(b)s(e)f(a)g(real)g(n)m (um)m(b)s(er)g(suc)m(h)i(that)e Fv(\013)j(<)35 1165 y Fw(inf)153 1085 y Fp(\000)199 1165 y Fv(\013)q Fw(\()p Fv(!)361 1180 y Fr(1)400 1165 y Fw(\))p Fv(;)17 b(\013)q Fw(\()p Fv(!)644 1180 y Fr(2)682 1165 y Fw(\))720 1085 y Fp(\001)804 1165 y Fw(and)38 b Fv(')f Fw(an)h(\()p Fv(!)1340 1180 y Fr(1)1405 1165 y Fs(\010)26 b Fv(!)1569 1180 y Fr(2)1608 1165 y Fw(\)-admissible)35 b(function)i(on)h Fv(M)2778 1180 y Fr(1)2844 1165 y Fs(\002)26 b Fv(M)3041 1180 y Fr(2)3081 1165 y Fw(.)59 b(If)37 b Fv(m)3354 1180 y Fr(2)3432 1165 y Fw(is)g(in)g Fv(M)3748 1180 y Fr(2)3788 1165 y Fw(,)35 1305 y(the)d(function)f(whic)m(h)g(sends)i Fv(m)1213 1320 y Fr(1)1286 1305 y Fw(to)e Fv(')p Fw(\()p Fv(m)1593 1320 y Fr(1)1632 1305 y Fv(;)17 b(m)1761 1320 y Fr(2)1801 1305 y Fw(\))33 b(is)f Fv(!)2031 1320 y Fr(1)2071 1305 y Fw(-admissible.)42 b(The)34 b(same)f(holds)g(for)g Fv(M)3561 1320 y Fr(1)3601 1305 y Fw(.)45 b(Let)35 1444 y(\()p Fv(u;)17 b(v)t Fw(\))32 b(in)g Fv(M)502 1459 y Fr(1)564 1444 y Fs(\002)22 b Fv(M)757 1459 y Fr(2)829 1444 y Fw(b)s(e)33 b(suc)m(h)h(that)f Fv(')p Fw(\()p Fv(u;)17 b(v)t Fw(\))26 b Fs(\025)i Fw(0.)43 b(Then)267 1535 y Fp(Z)323 1761 y Ft(M)391 1770 y Fg(1)425 1761 y Fo(\002)p Ft(M)548 1770 y Fg(2)603 1671 y Fv(e)648 1630 y Fo(\000)p Ft(\013')p Fr(\()p Ft(m)883 1639 y Fg(1)919 1630 y Ft(;m)1001 1639 y Fg(2)1035 1630 y Fr(\))1067 1671 y Fv(dV)1175 1686 y Fr(1)1231 1671 y Fv(dV)1339 1686 y Fr(2)1405 1671 y Fw(=)1509 1535 y Fp(Z)1564 1761 y Ft(M)1632 1770 y Fg(1)1687 1671 y Fv(e)1732 1630 y Fo(\000)p Ft(\013')p Fr(\()p Ft(m)1967 1639 y Fg(1)2003 1630 y Ft(;v)r Fr(\))2091 1530 y Fp(\022)2181 1535 y(Z)2236 1761 y Ft(M)2304 1770 y Fg(2)2360 1671 y Fv(e)2405 1625 y Fo(\000)p Ft(\013)2505 1544 y Fp(\002)2547 1625 y Ft(')p Fr(\()p Ft(m)2682 1634 y Fg(1)2717 1625 y Ft(;m)2799 1634 y Fg(2)2834 1625 y Fr(\))p Fo(\000)p Ft(')p Fr(\()p Ft(m)3051 1634 y Fg(1)3086 1625 y Ft(;v)r Fr(\))3169 1544 y Fp(\003)3216 1671 y Fv(dV)3324 1686 y Fr(2)3363 1530 y Fp(\023)3436 1671 y Fv(dV)3544 1686 y Fr(1)1405 1949 y Fs(\024)29 b Fv(C)1581 1964 y Fr(2)1636 1813 y Fp(Z)1692 2039 y Ft(M)1760 2048 y Fg(1)1815 1949 y Fv(e)1860 1907 y Fo(\000)p Ft(\013')p Fr(\()p Ft(m)2095 1916 y Fg(1)2131 1907 y Ft(;v)r Fr(\))2219 1949 y Fv(dV)2327 1964 y Fr(1)2393 1949 y Fs(\024)f Fv(C)2568 1964 y Fr(1)2624 1949 y Fv(C)2694 1964 y Fr(2)2734 1949 y Fv(:)35 2190 y Fw(Th)m(us,)35 b Fv(\013)28 b Fs(\024)g Fv(\013)568 2109 y Fp(\000)614 2190 y Fv(!)675 2205 y Fr(1)736 2190 y Fs(\010)22 b Fv(!)896 2205 y Fr(2)936 2109 y Fp(\001)1014 2190 y Fw(and)32 b(w)m(e)i(get)f(inf)1628 2109 y Fp(\000)1673 2190 y Fv(\013)q Fw(\()p Fv(!)1835 2205 y Fr(1)1874 2190 y Fw(\))p Fv(;)17 b(\013)q Fw(\()p Fv(!)2118 2205 y Fr(2)2157 2190 y Fw(\))2195 2109 y Fp(\001)2268 2190 y Fs(\024)28 b Fv(\013)2436 2109 y Fp(\000)2481 2190 y Fv(!)2542 2205 y Fr(1)2604 2190 y Fs(\010)22 b Fv(!)2764 2205 y Fr(2)2804 2109 y Fp(\001)2849 2190 y Fw(.)p 3744 2190 4 66 v 3748 2127 59 4 v 3748 2190 V 3806 2190 4 66 v 35 2410 a Fx(3.3.)57 b(Tian's)49 b(in)m(v)-6 b(arian)m(t)49 b(on)h Fv(G)1343 2425 y Ft(p;q)1436 2410 y Fw(\()p Fq(C)37 b Fw(\))p Fx(.)50 b(|)71 b Fw(Since)43 b(there)h(is)e(a)h(natural)f(dualit)m(y)g (isomorphism)35 2550 y(b)s(et)m(w)m(een)35 b Fv(G)489 2565 y Ft(p;q)582 2550 y Fw(\()p Fq(C)i Fw(\))h(and)33 b Fv(G)1046 2565 y Ft(q)r(;p)1139 2550 y Fw(\()p Fq(C)k Fw(\),)h(w)m(e)c(can)e(assume)i(that)e Fv(p)c Fs(\024)g Fv(q)36 b Fw(without)c(loss)g(of)h(generalit)m(y)-8 b(.)35 2736 y Fu(3.3.1.)49 b(Imb)-5 b(e)g(dding)49 b(of)932 2655 y Fp(\010)990 2736 y Fq(P)1049 2700 y Fr(1)1090 2736 y Fw(\()p Fq(C)20 b Fw(\))1232 2655 y Fp(\011)1296 2677 y Ft(p)1386 2736 y Fu(into)51 b Fv(G)1681 2751 y Ft(p;q)1774 2736 y Fw(\()p Fq(C)37 b Fw(\))56 b Fu(when)50 b Fv(p)57 b Fs(\024)g Fv(q)t Fw(.)43 b(|)72 b(F)-8 b(or)49 b Fv(w)j Fw(in)d Fq(C)3304 2700 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3529 2736 y Fw(,)54 b Fv(w)59 b Fw(=)35 2815 y Fp(\000)81 2896 y Fv(w)151 2911 y Ft(i;j)231 2815 y Fp(\001)301 2947 y Fg(1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)297 2999 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)341 3051 y(i)p Ff(6)p Fg(=)p Fe(j)512 2896 y Fw(,)32 b(w)m(e)i(de\014ne)g (the)f(map)40 b(~)-58 b Fv(\032)1431 2911 y Ft(w)1521 2896 y Fw(from)1751 2785 y Fp(n)1833 2896 y Fq(C)1899 2860 y Fr(2)1967 2896 y Fs(n)22 b Fw(\(0)p Fv(;)17 b Fw(0\))2240 2785 y Fp(o)2306 2808 y Ft(p)2378 2896 y Fw(to)32 b Fv(M)2591 2911 y Ft(p)p Fr(+)p Ft(q)r(;p)2775 2896 y Fw(\()p Fq(C)37 b Fw(\))h(b)m(y)704 3352 y(~)-57 b Fv(\032)746 3367 y Ft(w)802 3242 y Fp(\020)862 3352 y Fw(\()p Fv(\025)957 3367 y Ft(i)985 3352 y Fv(;)17 b(\026)1088 3367 y Ft(i)1116 3352 y Fw(\))1154 3367 y Fr(1)p Fo(\024)p Ft(i)p Fo(\024)p Ft(p)1362 3242 y Fp(\021)1449 3352 y Fw(=)1553 3118 y Fp(8)1553 3208 y(>)1553 3238 y(<)1553 3417 y(>)1553 3447 y(:)1650 3216 y Fv(\025)1707 3231 y Ft(i)1752 3216 y Fv(\016)1795 3231 y Ft(ij)2116 3216 y Fw(if)114 b Fv(i)28 b Fs(\024)g Fv(p)1650 3355 y(w)1720 3370 y Ft(i)p Fo(\000)p Ft(p;j)1907 3355 y Fv(\025)1964 3370 y Ft(j)2116 3355 y Fw(if)114 b Fv(i)28 b(>)g(p)k Fw(and)h Fv(i)28 b Fs(6)p Fw(=)f Fv(j)h Fw(+)22 b Fv(p)1650 3495 y(\026)1709 3510 y Ft(i)2116 3495 y Fw(if)114 b Fv(i)28 b(>)g(p)k Fw(and)h Fv(i)28 b Fw(=)f Fv(j)h Fw(+)22 b Fv(p)35 3698 y Fw(W)-8 b(e)23 b(mak)m(e,)i(for)d Fv(p)r Fw(+)r(1)k Fs(\024)i Fv(i)g Fs(\024)h Fv(p)r Fw(+)r Fv(q)t Fw(,)23 b(the)g(follo)m(wing)d(ro)m(w)i(transformations:)37 b Fv(L)2846 3713 y Ft(i)2902 3698 y Fs( )28 b Fv(L)3096 3713 y Ft(i)3126 3698 y Fs(\000)3236 3604 y Fp(X)3214 3805 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)3220 3861 y(i)p Ff(6)p Fg(=)p Fe(j)s Fg(+)p Fe(p)3428 3698 y Fv(w)3498 3713 y Ft(i)p Fo(\000)p Ft(p;j)3685 3698 y Fv(L)3751 3713 y Ft(j)3788 3698 y Fw(.)35 3974 y(W)-8 b(e)31 b(get)g(a)f(matrix) 756 3893 y Fp(\000)802 3974 y Fv(c)844 3989 y Ft(ij)904 3893 y Fp(\001)960 4025 y Fg(1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(p)p Fg(+)p Fe(q)995 4077 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)1266 3974 y Fw(with)g Fv(c)1528 3989 y Ft(ij)1616 3974 y Fw(=)e Fv(\016)1763 3989 y Ft(ij)1840 3974 y Fv(\025)1897 3989 y Ft(i)1955 3974 y Fw(if)i(1)d Fs(\024)h Fv(i)g Fs(\024)g Fv(p)j Fw(and)f Fv(c)2699 3989 y Ft(ij)2788 3974 y Fw(=)d Fv(\016)2934 3989 y Ft(i)p Fo(\000)p Ft(p;j)3121 3974 y Fv(\026)3180 3989 y Ft(j)3247 3974 y Fw(if)i Fv(p)18 b Fw(+)g(1)27 b Fs(\024)i Fv(i)e Fs(\024)35 4182 y Fv(p)c Fw(+)f Fv(q)t Fw(,)32 b(whic)m(h)i(has)f(rank) g Fv(p)p Fw(.)53 b(~)-58 b Fv(\032)1160 4197 y Ft(w)1249 4182 y Fw(induces)34 b(a)e(map)g(from)2126 4102 y Fp(\010)2184 4182 y Fq(P)2243 4146 y Fr(1)2284 4182 y Fw(\()p Fq(C)20 b Fw(\))2426 4102 y Fp(\011)2490 4124 y Ft(p)2563 4182 y Fw(in)m(to)32 b Fv(G)2838 4197 y Ft(p;q)2931 4182 y Fw(\()p Fq(C)37 b Fw(\))h(as)33 b(sho)m(wn)h(on)e(the)35 4342 y(follo)m(wing)21 b(diagram,)j(where)h Fv(\015)j Fw(is)c(the)g(pro)5 b(jection)23 b(of)g(the)h(principal)e(\014b)s(er)i (bundle)3079 4232 y Fp(n)3129 4342 y Fq(C)3195 4306 y Fr(2)3244 4342 y Fs(n)t Fw(\(0)p Fv(;)17 b Fw(0\))3499 4232 y Fp(o)3565 4254 y Ft(p)3628 4342 y Fw(on)m(to)35 4422 y Fp(\010)94 4503 y Fq(P)153 4466 y Fr(1)194 4503 y Fw(\()p Fq(C)j Fw(\))336 4422 y Fp(\011)400 4444 y Ft(p)439 4503 y Fw(.)42 b(Remark)25 b(that)35 b(~)-58 b Fv(\032)1123 4518 y Ft(w)1206 4503 y Fw(sends)28 b([0)p Fv(;)17 b Fw(1])9 b Fs(\002)g(\001)17 b(\001)g(\001)6 b(\002)j Fw([0)p Fv(;)17 b Fw(1])26 b(on)m(to)g Fv(\031)t Fw(\()p Fv(A)p Fw(\),)h(where)h Fv(m)3020 4518 y Fo(f)p Ft(p)p Fr(+1)p Ft(;:::)n(;)p Fr(2)p Ft(p)p Fo(g)3389 4503 y Fw(\()p Fv(A)p Fw(\))g(=)g Fv(I)3721 4466 y Fr(\()p Ft(p)p Fr(\))35 4642 y Fw(and)33 b Fv(m)310 4658 y Fo(f)p Ft(p)p Fr(+1)p Ft(;:::)o(;)p Fr(2)p Ft(p)p Fo(g)676 4639 y Fe(c)712 4642 y Fw(\()p Fv(A)p Fw(\))27 b(=)h(0)1041 4606 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))1224 4642 y Fw(.)1251 4853 y Fp(\010)1310 4933 y Fq(C)1375 4897 y Fr(2)1443 4933 y Fs(n)22 b Fw(\(0)p Fv(;)17 b Fw(0\))1733 4853 y Fp(\011)1790 4875 y Ft(p)2064 4907 y Fc(/)p Fb(/)1915 4859 y Fr(~)-41 b Ft(\032)1945 4867 y Fe(w)p 1865 4909 200 4 v 1541 5202 a Fc(\017)p Fb(\017)1466 5111 y Ft(\015)p 1539 5202 4 200 v 2099 4932 a Fv(M)2203 4896 y Fo(\003)2243 4932 y Fw(\()p Fv(p)22 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\))2363 5212 y Fc(\017)p Fb(\017)2398 5117 y Ft(\031)p 2362 5212 4 221 v 1339 5243 a Fp(\010)1397 5324 y Fq(P)1456 5288 y Fr(1)1497 5324 y Fw(\()p Fq(C)j Fw(\))1639 5243 y Fp(\011)1703 5266 y Ft(p)2161 5298 y Fc(/)p Fb(/)1909 5362 y Ft(\032)1945 5370 y Fe(w)p 1778 5300 384 4 v 2196 5322 a Fv(G)2273 5337 y Ft(p;q)2366 5322 y Fw(\()p Fq(C)37 b Fw(\))p eop %%Page: 9 9 9 8 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h (GRASSMANN)d(MANIF)n(OLD)804 b Fk(9)35 619 y Fw(W)-8 b(e)33 b(ha)m(v)m(e)311 727 y Fp(\000)357 808 y Fv(\031)26 b Fs(\016)31 b Fw(~)-58 b Fv(\032)560 823 y Ft(w)617 727 y Fp(\001)662 749 y Fo(\003)702 727 y Fp(\000)715 808 y Fh(G)832 838 y Ft(p;q)926 727 y Fp(\001)999 808 y Fw(=)27 b Fv(i)17 b(@)p 1208 726 57 4 v 5 w(@)40 b Fw(log)1425 697 y Fp(\020)1485 808 y Fw(det)1620 727 y Fp(\000)1666 749 y Ft(t)1688 808 y Fw(~)-58 b Fv(\032)1729 823 y Ft(w)p 1803 730 34 4 v 1795 808 a Fw(~)g Fv(\032)1836 831 y Ft(w)1893 727 y Fp(\001)1938 697 y(\021)999 1090 y Fw(=)27 b Fv(i)17 b(@)p 1208 1009 57 4 v 5 w(@)40 b Fw(log)1425 920 y Fp( )1644 1016 y Fw(det)1796 935 y Fp(\000)1842 958 y Ft(t)1864 1016 y Fw(~)-58 b Fv(\032)1905 1031 y Ft(w)p 1979 938 34 4 v 1971 1016 a Fw(~)g Fv(\032)2012 1040 y Ft(w)2069 935 y Fp(\001)p 1514 1067 731 4 v 1561 1117 a Ft(p)1515 1151 y Fp(Y)1514 1364 y Ft(k)r Fr(=1)1643 1165 y Fp(\000)1689 1246 y Fs(j)p Fv(\025)1774 1261 y Ft(k)1816 1246 y Fs(j)1844 1205 y Fr(2)1905 1246 y Fw(+)22 b Fs(j)p Fv(\026)2090 1261 y Ft(k)2132 1246 y Fs(j)2160 1205 y Fr(2)2199 1165 y Fp(\001)2255 920 y(!)2356 1090 y Fw(+)2508 961 y Ft(p)2454 995 y Fp(X)2461 1207 y Ft(k)r Fr(=1)2614 1090 y Fv(i)17 b(@)p 2720 1009 57 4 v 5 w(@)40 b Fw(log)2937 1009 y Fp(\000)2983 1090 y Fs(j)p Fv(\025)3068 1105 y Ft(k)3110 1090 y Fs(j)3138 1049 y Fr(2)3199 1090 y Fw(+)22 b Fs(j)p Fv(\026)3384 1105 y Ft(k)3426 1090 y Fs(j)3454 1049 y Fr(2)3494 1009 y Fp(\001)999 1508 y Fw(=)27 b Fv(i)17 b(@)p 1208 1427 V 5 w(@)40 b Fw(log)1453 1483 y(~)1442 1508 y(\010)23 b(+)f Fv(\015)1689 1467 y Fo(\003)1728 1427 y Fp(\000)1774 1508 y Fv(F)14 b(S)1911 1523 y Fr(1)1972 1508 y Fs(\010)23 b(\001)17 b(\001)g(\001)j(\010)j Fv(F)14 b(S)2447 1523 y Fr(1)2486 1427 y Fp(\001)2531 1508 y Fv(;)35 1702 y Fw(where)47 b Fv(F)14 b(S)467 1717 y Fr(1)552 1702 y Fw(is)45 b(the)h(F)-8 b(ubini-Study)45 b(metric)g(on)g Fq(P)1971 1666 y Fr(1)2012 1702 y Fw(\()p Fq(C)20 b Fw(\).)2281 1677 y(~)2270 1702 y(\010)46 b(is)f(in)m(v)-5 b(arian)m(t)45 b(b)m(y)h(the)g(action)f(of)g(the)35 1842 y(structural)34 b(group)g Fq(C)831 1806 y Fo(\003)899 1842 y Fs(\002)23 b(\001)17 b(\001)g(\001)22 b(\002)h Fq(C)1305 1806 y Fo(\003)1350 1842 y Fw(,)35 b(so)f(it)e(induces)j(a)f (map)f(\010)h(from)2616 1761 y Fp(\010)2674 1842 y Fq(P)2733 1806 y Fr(1)2775 1842 y Fw(\()p Fq(C)20 b Fw(\))2917 1761 y Fp(\011)2981 1784 y Ft(p)3054 1842 y Fw(in)m(to)33 b Fq(C)20 b Fw(.)53 b(Note)34 b(that)35 1981 y(\010)105 1901 y Fp(\000)152 1981 y Fw([0)p Fv(;)17 b Fw(1])k Fs(\002)h(\001)17 b(\001)g(\001)i(\002)j Fw([0)p Fv(;)17 b Fw(1])900 1901 y Fp(\001)973 1981 y Fw(=)28 b(1.)43 b(Then)1450 1901 y Fp(\000)1496 1981 y Fv(\031)25 b Fs(\016)30 b Fw(~)-57 b Fv(\032)1698 1996 y Ft(w)1754 1901 y Fp(\001)1800 1923 y Fo(\003)1840 1901 y Fp(\000)1853 1981 y Fh(G)1970 2012 y Ft(p;q)2063 1901 y Fp(\001)2137 1981 y Fw(=)27 b Fv(\031)2299 1945 y Fo(\003)2339 1901 y Fp(\000)2384 1981 y Fv(i)17 b(@)p 2490 1900 V 5 w(@)40 b Fw(log)17 b(\010)22 b(+)f Fv(F)14 b(S)3050 1996 y Fr(1)3111 1981 y Fs(\010)22 b(\001)17 b(\001)g(\001)j(\010)i Fv(F)14 b(S)3584 1996 y Fr(1)3623 1901 y Fp(\001)3668 1981 y Fw(,)33 b(so)35 2122 y(that)g Fv(\032)297 2086 y Fo(\003)297 2147 y Ft(w)354 2041 y Fp(\000)367 2122 y Fh(G)484 2153 y Ft(p;q)577 2041 y Fp(\001)651 2122 y Fw(=)27 b Fv(i)17 b(@)p 860 2041 V 5 w(@)40 b Fw(log)17 b(\010)22 b(+)g Fv(F)14 b(S)1421 2137 y Fr(1)1483 2122 y Fs(\010)22 b(\001)17 b(\001)g(\001)k(\010)h Fv(F)14 b(S)1957 2137 y Fr(1)1996 2122 y Fw(.)35 2308 y Fu(3.3.2.)49 b(L)-5 b(ower)52 b(b)-5 b(ound)51 b(of)h Fv(\013)q Fw(\()-33 b Fh(G)1248 2339 y Ft(p;q)1341 2308 y Fw(\).)43 b(|)73 b(F)-8 b(or)50 b Fv(I)59 b Fw(in)51 b Fs(I)7 b Fw(,)56 b(w)m(e)c(de\014ne)h Fv(P)2718 2323 y Ft(I)2809 2308 y Fw(b)m(y)f Fv(m)3048 2323 y Ft(I)3088 2308 y Fw(\()p Fv(P)3189 2323 y Ft(I)3229 2308 y Fw(\))59 b(=)g Fv(I)3512 2272 y Fr(\()p Ft(p)p Fr(\))3658 2308 y Fw(and)35 2448 y Fv(m)120 2463 y Ft(I)156 2444 y Fe(c)193 2448 y Fw(\()p Fv(P)294 2463 y Ft(I)333 2448 y Fw(\))52 b(=)f(0)599 2411 y Fr(\()p Ft(q)r Fo(\002)p Ft(p)p Fr(\))782 2448 y Fw(.)86 b(If)46 b Fv(n)52 b Fw(=)1243 2367 y Fp(\000)1289 2403 y Ft(p)p Fr(+)p Ft(q)1333 2482 y(p)1413 2367 y Fp(\001)1459 2448 y Fw(,)e(w)m(e)d(set)g(\001)1940 2463 y Ft(n)2039 2448 y Fw(=)2166 2367 y Fp(\010)2225 2448 y Fv(P)2288 2463 y Ft(I)2327 2367 y Fp(\011)2385 2487 y Ft(I)5 b Fo(2I)2516 2448 y Fw(.)85 b(Since)47 b Fv(U)10 b Fw(\()p Fv(p)32 b Fw(+)g Fv(q)t Fw(\))46 b(is)g(a)g(transi-)35 2587 y(tiv)m(e)41 b(group)g(of)f(holomorphic)f(isometries)g(of)h Fv(G)1864 2602 y Ft(p;q)1957 2587 y Fw(\()p Fq(C)d Fw(\),)49 b(w)m(e)41 b(kno)m(w)h(from)e(prop)s(osition)f(\(3.1\),)j(that)35 2727 y Fv(\013)98 2646 y Fp(\000)111 2727 y Fh(G)229 2757 y Ft(p;q)322 2646 y Fp(\001)404 2727 y Fw(=)36 b Fv(\013)578 2753 y Fg(\001)628 2761 y Fe(n)678 2646 y Fp(\000)691 2727 y Fh(G)809 2757 y Ft(p;q)902 2646 y Fp(\001)948 2727 y Fw(.)58 b(W)-8 b(e)38 b(set)g Fv(I)44 b Fw(=)36 b Fs(f)p Fv(p)26 b Fw(+)f(1)p Fv(;)17 b(:)g(:)g(:)e(;)i Fw(2)p Fv(p)p Fs(g)p Fw(.)58 b(Let)38 b Fv(')f Fw(b)s(e)h(an)f (admissible)f(function)h(on)35 2866 y Fv(G)112 2881 y Ft(p;q)206 2866 y Fw(\()p Fq(C)f Fw(\),)45 b(nonnegativ)m(e)38 b(on)g(\001)1205 2881 y Ft(n)1252 2866 y Fw(.)59 b(The)39 b(last)e(equalit)m(y)g(of)h(the)g(preceden)m(t)i(section)e(sho)m(ws)h (that)e(the)35 3006 y(function)25 b Fv(')6 b Fs(\016)g Fv(\032)586 3021 y Ft(w)648 3006 y Fw(+)g(log)16 b(\010)25 b(is)1057 2925 y Fp(\000)1103 3006 y Fv(F)14 b(S)1240 3021 y Fr(1)1285 3006 y Fs(\010)6 b(\001)17 b(\001)g(\001)t(\010)6 b Fv(F)14 b(S)1710 3021 y Fr(1)1749 2925 y Fp(\001)1795 3006 y Fw(-admissible)22 b(for)i(ev)m(ery)j Fv(w)f Fw(in)e Fq(C)2963 2969 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3188 3006 y Fw(.)40 b(F)-8 b(urthermore,)35 3064 y Fp(\000)81 3145 y Fv(')24 b Fs(\016)f Fv(\032)292 3160 y Ft(w)372 3145 y Fw(+)h(log)16 b(\010)684 3064 y Fp(\001)765 3145 y Fw(sends)36 b([0)p Fv(;)17 b Fw(1])23 b Fs(\002)h(\001)17 b(\001)g(\001)22 b(\002)i Fw([0)p Fv(;)17 b Fw(1])34 b(to)h(the)g(nonnegativ)m(e)g(n)m(um)m(b)s(er)g Fv(')p Fw(\()p Fv(P)3177 3171 y Fe(I)3216 3145 y Fw(\).)50 b(It)34 b(is)h(kno)m(wn)35 3284 y(that)e Fv(\013)q Fw(\()p Fv(F)14 b(S)485 3299 y Fr(1)524 3284 y Fw(\))27 b(=)h(1)k(\(see)i([)p Fx(Au3)p Fw(]\).)43 b(Prop)s(osition)31 b(\(3.4\))h(yields)g Fv(\013)2430 3204 y Fp(\000)2476 3284 y Fv(F)14 b(S)2613 3299 y Fr(1)2674 3284 y Fs(\010)22 b(\001)17 b(\001)g(\001)k(\010)h Fv(F)14 b(S)3148 3299 y Fr(1)3188 3204 y Fp(\001)3261 3284 y Fw(=)28 b(1.)35 3424 y(Let)43 b Fv(\013)h Fw(b)s(e)f(a)g(real)f (n)m(um)m(b)s(er)h(suc)m(h)h(that)f Fv(\013)j(<)f Fw(1.)74 b(There)44 b(exists)g(a)e(constan)m(t)i Fv(C)7 b Fw(,)45 b(indep)s(enden)m(t)f(of)35 3587 y Fv(')p Fw(,)g(suc)m(h)f(that)620 3452 y Fp(Z)675 3596 y(\010)733 3677 y Fa(P)779 3658 y Fg(1)809 3677 y Fr(\()p Fa(C)9 b Fr(\))905 3596 y Fp(\011)970 3613 y Fe(p)1026 3587 y Fv(e)1071 3546 y Fo(\000)p Ft(\013')p Fo(\016)p Ft(\032)1288 3554 y Fe(w)1360 3587 y Fw(\010)1430 3546 y Fo(\000)p Ft(\013)1578 3587 y Fs(\024)44 b Fv(C)7 b Fw(.)70 b(W)-8 b(e)42 b(de\014ne)h(the)f(map)f Fv(F)2807 3602 y Ft(I)2889 3587 y Fw(from)f Fv(\031)t Fw(\()p Fv(U)3291 3602 y Ft(I)3331 3587 y Fw(\))i(to)f Fq(R)3605 3602 y Fr(+)3712 3587 y Fw(b)m(y)35 3808 y Fv(F)98 3823 y Ft(I)139 3808 y Fw(\()p Fv(Z)244 3823 y Ft(I)283 3808 y Fw(\))28 b(=)f(det)604 3728 y Fp(\000)650 3808 y Fv(I)8 b(d)19 b Fw(+)847 3772 y Ft(t)879 3808 y Fv(Z)946 3823 y Ft(I)p 1002 3728 58 4 v 985 3808 a Fv(Z)1059 3823 y Ft(I)1099 3728 y Fp(\001)1145 3808 y Fw(.)43 b(On)1376 3728 y Fp(\010)1434 3808 y Fq(P)1493 3772 y Fr(1)1534 3808 y Fw(\()p Fq(C)20 b Fw(\))1676 3728 y Fp(\011)1740 3750 y Ft(p)1780 3808 y Fw(,)31 b(w)m(e)h(w)m(ork)g(with)f(the)h(co)s(ordinates)e Fv(\026)3180 3823 y Fr(1)3219 3808 y Fv(;)17 b(:)g(:)g(:)f(;)h(\026) 3497 3823 y Ft(p)3567 3808 y Fw(in)30 b(the)35 3948 y(c)m(hart)j Fv(\025)344 3963 y Fr(1)411 3948 y Fw(=)28 b Fs(\001)17 b(\001)g(\001)26 b Fw(=)h Fv(\025)819 3963 y Ft(p)887 3948 y Fw(=)g(1.)43 b(Th)m(us)46 4191 y(\010\()p Fv(\026)p Fw(\))28 b(=)466 4124 y Fv(F)529 4139 y Ft(I)591 4124 y Fs(\016)22 b Fv(\032)713 4139 y Ft(w)770 4124 y Fw(\()p Fv(\026)p Fw(\))p 392 4168 586 4 v 439 4219 a Ft(p)393 4253 y Fp(Y)392 4465 y Ft(k)r Fr(=1)521 4267 y Fp(\000)567 4347 y Fw(1)g(+)g Fs(j)p Fv(\026)823 4362 y Ft(k)865 4347 y Fs(j)893 4306 y Fr(2)932 4267 y Fp(\001)987 4191 y Fv(;)115 b Fw(so)32 b(that)1541 4056 y Fp(Z)1597 4281 y Ft(\026)p Fo(2)p Fa(C)1739 4262 y Fe(p)1802 4191 y Fv(e)1847 4150 y Fo(\000)p Ft(\013')p Fo(\016)p Ft(\032)2064 4158 y Fe(w)2115 4150 y Fr(\()p Ft(\026)p Fr(\))2718 4117 y Fv(dV)2826 4132 y Ft(\026)2872 4037 y Fp(\000)2918 4117 y Fq(C)2996 4081 y Ft(p)3041 4037 y Fp(\001)p 2243 4168 1321 4 v 2289 4219 a Ft(p)2244 4253 y Fp(Y)2243 4465 y Ft(k)r Fr(=1)2371 4267 y Fp(\000)2417 4347 y Fw(1)22 b(+)g Fs(j)p Fv(\026)2673 4362 y Ft(k)2715 4347 y Fs(j)2743 4306 y Fr(2)2782 4267 y Fp(\001)2828 4289 y Fr(2)p Fo(\000)p Ft(\013)2984 4267 y Fp(\000)3030 4347 y Fv(F)3093 4373 y Fe(I)3154 4347 y Fs(\016)g Fv(\032)3276 4362 y Ft(w)3333 4347 y Fw(\()p Fv(\026)p Fw(\))3468 4267 y Fp(\001)3513 4289 y Ft(\013)3600 4191 y Fs(\024)29 b Fv(C)r(:)p eop %%Page: 10 10 10 9 bop 35 283 a Fk(10)1446 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 687 y Fw(W)h(e)38 b(ha)m(v)m(e)h(the)f(inequalit)m(y)1123 558 y Ft(q)1068 592 y Fp(X)1083 802 y Ft(i)p Fr(=1)1283 558 y Ft(p)1228 592 y Fp(X)1239 802 y Ft(j)t Fr(=1)1372 602 y Fp(\014)1372 662 y(\014)1406 687 y Fv(Z)1473 702 y Ft(ij)1533 602 y Fp(\014)1533 662 y(\014)1566 628 y Fr(2)1641 687 y Fs(\024)f Fv(F)1818 702 y Ft(I)1858 606 y Fp(\000)1903 687 y Fv(P)1966 702 y Ft(I)2006 606 y Fp(\001)2052 687 y Fw(.)58 b(In)37 b(particular,)g(for)g(ev)m(ery)i Fv(k)h Fw(in)d Fs(f)p Fw(1)p Fv(;)17 b(:)g(:)g(:)e(;)i(p)p Fs(g)p Fw(,)35 938 y(1)g(+)g Fs(j)p Fv(\026)281 953 y Ft(k)323 938 y Fs(j)351 902 y Fr(2)418 938 y Fs(\024)28 b Fv(f)571 953 y Ft(I)628 938 y Fs(\016)17 b Fv(\032)745 953 y Ft(w)802 938 y Fw(\()p Fv(\026)p Fw(\),)30 b(and)h Fv(f)1230 953 y Ft(I)1287 938 y Fs(\016)17 b Fv(\032)1404 953 y Ft(w)1461 938 y Fw(\()p Fv(\026)p Fw(\))27 b Fs(\025)h Fw(1)17 b(+)1928 843 y Fp(X)1911 1044 y Fg(1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)1907 1097 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)1951 1150 y(i)p Ff(6)p Fg(=)p Fe(j)2113 853 y Fp(\014)2113 913 y(\014)2147 938 y Fv(w)2217 953 y Ft(ij)2277 853 y Fp(\014)2277 913 y(\014)2310 880 y Fr(2)2349 938 y Fw(.)43 b(Th)m(us,)32 b(for)e Fv(\024)e(>)f Fw(0)j(and)g Fv(w)g Fs(2)f Fq(C)3563 902 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3788 938 y Fw(,)175 1266 y Ft(p)129 1299 y Fp(Y)128 1512 y Ft(k)r Fr(=1)257 1313 y Fp(\000)303 1394 y Fw(1)21 b(+)h Fs(j)p Fv(\026)558 1409 y Ft(k)600 1394 y Fs(j)628 1353 y Fr(2)668 1313 y Fp(\001)713 1336 y Fr(2)p Fo(\000)p Ft(\013)p 63 1538 855 4 v 63 1567 a Fp(\000)109 1648 y Fv(F)172 1663 y Ft(I)234 1648 y Fs(\016)g Fv(\032)356 1663 y Ft(w)413 1648 y Fw(\()p Fv(\026)p Fw(\))548 1567 y Fp(\001)593 1590 y Ft(\024)p Fr(+)p Ft(p)p Fr(+)p Ft(q)r Fo(\000)p Ft(\013)955 1560 y Fs(\024)1563 1493 y Fw(1)p 1070 1538 1035 4 v 1070 1577 a Fp(\000)1116 1658 y Fv(F)1179 1684 y Fe(I)1241 1658 y Fs(\016)g Fv(\032)1363 1673 y Ft(w)1420 1658 y Fw(\()p Fv(\026)p Fw(\))1555 1577 y Fp(\001)1600 1599 y Ft(\024)p Fo(\000)p Ft(p)p Fr(+)p Ft(q)r Fr(+)p Ft(\013)p Fr(\()p Ft(p)p Fo(\000)p Fr(1\))2142 1560 y Fs(\024)2631 1493 y Fw(1)p 2257 1538 796 4 v 2257 1556 a Fp(\020)2317 1666 y Fw(1)g(+)2527 1572 y Fp(X)2510 1773 y Fg(1)p Ff(\024)p Fe(i)p Ff(\024)p Fe(q)2506 1825 y Fg(1)p Ff(\024)p Fe(j)s Ff(\024)p Fe(p)2551 1879 y(i)p Ff(6)p Fg(=)p Fe(j)2712 1582 y Fp(\014)2712 1641 y(\014)2746 1666 y Fv(w)2816 1681 y Ft(ij)2876 1582 y Fp(\014)2876 1641 y(\014)2909 1608 y Fr(2)2949 1556 y Fp(\021)3008 1578 y Ft(\024)3090 1560 y Fw(=)3457 1493 y(1)p 3204 1538 556 4 v 3204 1556 a Fp(\020)3263 1666 y Fw(1)g(+)3432 1582 y Fp(\015)3432 1641 y(\015)3488 1666 y Fv(w)3561 1582 y Fp(\015)3561 1641 y(\015)3616 1608 y Fr(2)3655 1556 y Fp(\021)3714 1578 y Ft(\024)3769 1560 y Fs(\001)35 2030 y Fw(W)-8 b(e)33 b(ha)m(v)m(e,)h(according)e(to)h(Prop)s(osition)d(\(2.3\),)192 2130 y Fp(Z)248 2356 y Ft(\031)r Fr(\()p Ft(U)366 2367 y Fe(I)401 2356 y Fr(\))459 2198 y Fv(e)504 2162 y Fo(\000)p Ft(\013')p 459 2243 196 4 v 496 2334 a Fv(F)573 2300 y Ft(\024)559 2361 y(I)692 2266 y Fw(=)796 2130 y Fp(Z)851 2356 y Ft(w)r Fo(2)p Fa(C)1004 2336 y Fe(p)p Fg(\()p Fe(q)r Ff(\000)p Fg(1\))1223 2130 y Fp(Z)1278 2356 y Ft(\026)p Fo(2)p Fa(C)1421 2337 y Fe(p)1663 2198 y Fv(e)1708 2162 y Fo(\000)p Ft(\013')p Fo(\016)p Ft(\032)1925 2170 y Fe(w)1976 2162 y Fr(\()p Ft(\026)p Fr(\))p 1493 2243 754 4 v 1493 2272 a Fp(\000)1539 2353 y Fv(F)1602 2368 y Ft(I)1664 2353 y Fs(\016)22 b Fv(\032)1786 2368 y Ft(w)1843 2353 y Fw(\()p Fv(\026)p Fw(\))1978 2272 y Fp(\001)2023 2295 y Ft(\024)p Fr(+)p Ft(p)p Fr(+)p Ft(q)2274 2266 y Fv(dV)2382 2281 y Ft(\026)2428 2185 y Fp(\000)2474 2266 y Fq(C)2551 2224 y Ft(p)2597 2185 y Fp(\001)2659 2266 y Fv(dV)2767 2281 y Ft(w)2823 2185 y Fp(\000)2869 2266 y Fq(C)2947 2224 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3171 2185 y Fp(\001)301 2691 y Fw(=)405 2556 y Fp(Z)460 2781 y Ft(w)r Fo(2)p Fa(C)612 2762 y Fe(p)p Fg(\()p Fe(q)r Ff(\000)p Fg(1)q(\))831 2556 y Fp(Z)887 2781 y Ft(\026)p Fo(2)p Fa(C)1029 2762 y Fe(p)1075 2521 y Fp( )1617 2624 y Fv(e)1662 2588 y Fo(\000)p Ft(\013')p Fo(\016)p Ft(\032)1879 2596 y Fe(w)1930 2588 y Fr(\()p Ft(\026)p Fr(\))p 1164 2668 1321 4 v 1211 2719 a Ft(p)1165 2753 y Fp(Y)1164 2965 y Ft(k)r Fr(=1)1293 2767 y Fp(\000)1338 2848 y Fw(1)g(+)g Fs(j)p Fv(\026)1594 2863 y Ft(k)1636 2848 y Fs(j)1664 2806 y Fr(2)1703 2767 y Fp(\001)1749 2789 y Fr(2)p Fo(\000)p Ft(\013)1905 2767 y Fp(\000)1951 2848 y Fv(F)2014 2863 y Ft(I)2076 2848 y Fs(\016)g Fv(\032)2198 2863 y Ft(w)2255 2848 y Fw(\()p Fv(\026)p Fw(\))2390 2767 y Fp(\001)2435 2789 y Ft(\013)2495 2521 y Fp(!)1379 3249 y Fs(\002)1600 2954 y Ft(p)1554 2988 y Fp(Y)1553 3200 y Ft(k)r Fr(=1)1682 3002 y Fp(\000)1728 3082 y Fw(1)g(+)g Fs(j)p Fv(\026)1984 3097 y Ft(k)2026 3082 y Fs(j)2054 3041 y Fr(2)2093 3002 y Fp(\001)2138 3024 y Fr(2)p Fo(\000)p Ft(\013)p 1489 3226 855 4 v 1489 3256 a Fp(\000)1534 3336 y Fv(F)1597 3351 y Ft(I)1659 3336 y Fs(\016)g Fv(\032)1781 3351 y Ft(w)1838 3336 y Fw(\()p Fv(\026)p Fw(\))1973 3256 y Fp(\001)2019 3278 y Ft(\024)p Fr(+)p Ft(p)p Fr(+)p Ft(q)r Fo(\000)p Ft(\013)2369 3249 y Fv(dV)2477 3264 y Ft(\026)2523 3168 y Fp(\000)2569 3249 y Fq(C)2647 3208 y Ft(p)2693 3168 y Fp(\001)2755 3249 y Fv(dV)2863 3264 y Ft(w)2919 3168 y Fp(\000)2965 3249 y Fq(C)3043 3208 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3267 3168 y Fp(\001)301 3674 y Fw(=)405 3539 y Fp(Z)460 3764 y Ft(w)r Fo(2)p Fa(C)612 3745 y Fe(p)p Fg(\()p Fe(q)r Ff(\000)p Fg(1)q(\))815 3504 y Fp( )894 3539 y(Z)949 3764 y Ft(\026)p Fo(2)p Fa(C)1091 3745 y Fe(p)1617 3607 y Fv(e)1662 3571 y Fo(\000)p Ft(\013')p Fo(\016)p Ft(\032)1879 3579 y Fe(w)1930 3571 y Fr(\()p Ft(\026)p Fr(\))p 1164 3652 1321 4 v 1211 3702 a Ft(p)1165 3736 y Fp(Y)1164 3948 y Ft(k)r Fr(=1)1293 3750 y Fp(\000)1338 3831 y Fw(1)g(+)g Fs(j)p Fv(\026)1594 3846 y Ft(k)1636 3831 y Fs(j)1664 3790 y Fr(2)1703 3750 y Fp(\001)1749 3772 y Fr(2)p Fo(\000)p Ft(\013)1905 3750 y Fp(\000)1951 3831 y Fv(F)2014 3857 y Fe(I)2076 3831 y Fs(\016)g Fv(\032)2198 3846 y Ft(w)2255 3831 y Fw(\()p Fv(\026)p Fw(\))2390 3750 y Fp(\001)2435 3772 y Ft(\013)2511 3674 y Fv(dV)2619 3689 y Ft(\026)2665 3594 y Fp(\000)2711 3674 y Fq(C)2789 3633 y Ft(p)2834 3594 y Fp(\001)2880 3504 y(!)2997 3674 y Fs(\002)3107 3601 y Fv(dV)3215 3616 y Ft(w)3271 3520 y Fp(\000)3317 3601 y Fq(C)3395 3565 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))3619 3520 y Fp(\001)p 3107 3652 558 4 v 3122 3684 a(\000)3168 3765 y Fw(1)g(+)3337 3680 y Fp(\015)3337 3740 y(\015)3392 3765 y Fv(w)3465 3680 y Fp(\015)3465 3740 y(\015)3520 3706 y Fr(2)3559 3684 y Fp(\001)3605 3706 y Ft(\024)301 4247 y Fs(\024)28 b Fv(C)500 4111 y Fp(Z)555 4337 y Ft(w)r Fo(2)p Fa(C)707 4317 y Fe(p)p Fg(\()p Fe(q)r Ff(\000)p Fg(1)q(\))937 4173 y Fv(dV)1045 4188 y Ft(w)1101 4092 y Fp(\000)1146 4173 y Fq(C)1224 4137 y Ft(p)p Fr(\()p Ft(q)r Fo(\000)p Fr(1\))1449 4092 y Fp(\001)p 937 4224 V 952 4256 a(\000)997 4337 y Fw(1)22 b(+)1166 4252 y Fp(\015)1166 4312 y(\015)1222 4337 y Fv(w)1295 4252 y Fp(\015)1295 4312 y(\015)1349 4279 y Fr(2)1389 4256 y Fp(\001)1434 4279 y Ft(\024)1532 4247 y Fs(\024)28 b Fv(C)1714 4206 y Fo(0)1932 4247 y Fw(if)k Fv(\024)c(>)f(p)p Fw(\()p Fv(q)f Fs(\000)d Fw(1\))p Fv(:)35 4573 y Fw(Th)m(us,)35 b(w)m(e)e(obtain)f(that)g(for)g(all)f Fv(I)40 b Fw(in)32 b Fs(I)7 b Fw(,)1571 4437 y Fp(Z)1626 4663 y Ft(\031)r Fr(\()p Ft(U)1744 4674 y Fe(I)1780 4663 y Fr(\))1838 4505 y Fv(e)1883 4469 y Fo(\000)p Ft(\013')p 1838 4550 196 4 v 1875 4641 a Fv(F)1952 4607 y Ft(\024)1938 4668 y(I)2071 4573 y Fs(\024)28 b Fv(C)7 b Fw(,)33 b(where)h Fv(C)39 b Fw(is)32 b(indep)s(enden)m(t)i(of)e Fv(')p Fw(.)35 4772 y(Since)g Fv(G)366 4787 y Ft(p;q)459 4772 y Fw(\()p Fq(C)37 b Fw(\))f(is)31 b(compact,)g(there)h(exists)g(a)f (family)2059 4692 y Fp(\000)2105 4772 y Fv(V)2162 4787 y Ft(I)2202 4692 y Fp(\001)2247 4811 y Ft(I)5 b Fo(2I)2409 4772 y Fw(of)31 b(op)s(en)g(sets)h(of)f Fv(G)3129 4787 y Ft(p;q)3222 4772 y Fw(\()p Fq(C)37 b Fw(\))g(suc)m(h)32 b(that)35 4912 y Fv(V)92 4927 y Ft(I)168 4912 y Fw(is)j(relativ)m(ely)g (compact)g(in)g Fv(\031)t Fw(\()p Fv(U)1371 4927 y Ft(I)1411 4912 y Fw(\))h(for)f(ev)m(ery)i Fv(I)k Fs(2)33 b(I)7 b Fw(,)38 b(and)2398 4837 y Fp(S)2481 4941 y Ft(I)5 b Fo(2)12 b(I)2640 4912 y Fv(V)2697 4927 y Ft(I)2770 4912 y Fw(=)33 b Fv(G)2956 4927 y Ft(p;q)3049 4912 y Fw(\()p Fq(C)k Fw(\).)58 b(There)37 b(exists)35 5051 y Fv(M)i(>)27 b Fw(0)33 b(suc)m(h)h(that)e Fv(F)847 5066 y Ft(I)915 5051 y Fs(\024)c Fv(M)43 b Fw(on)33 b Fv(V)1350 5066 y Ft(I)1422 5051 y Fw(for)f(ev)m(ery)j Fv(I)g Fs(2)28 b(I)7 b Fw(.)44 b(Th)m(us)70 5137 y Fp(Z)126 5362 y Ft(G)181 5370 y Fe(p;q)266 5362 y Fr(\()p Fa(C)27 b Fr(\))401 5272 y Fv(e)446 5231 y Fo(\000)p Ft(\013')625 5272 y Fs(\024)730 5177 y Fp(X)733 5389 y Ft(I)5 b Fo(2)11 b(I)890 5137 y Fp(Z)946 5362 y Ft(V)987 5373 y Fe(I)1043 5272 y Fv(e)1088 5231 y Fo(\000)p Ft(\013')1266 5272 y Fs(\024)1371 5177 y Fp(X)1374 5389 y Ft(I)5 b Fo(2)12 b(I)1532 5272 y Fv(M)1636 5231 y Ft(\024)1698 5137 y Fp(Z)1753 5362 y Ft(V)1794 5373 y Fe(I)1860 5205 y Fv(e)1905 5169 y Fo(\000)p Ft(\013')p 1860 5249 V 1897 5340 a Fv(F)1974 5306 y Ft(\024)1960 5367 y(I)2093 5272 y Fs(\024)29 b Fv(M)2303 5231 y Ft(\024)2365 5177 y Fp(X)2368 5389 y Ft(I)5 b Fo(2)11 b(I)2525 5137 y Fp(Z)2581 5362 y Ft(\031)r Fr(\()p Ft(U)2699 5373 y Fe(I)2734 5362 y Fr(\))2792 5205 y Fv(e)2837 5169 y Fo(\000)p Ft(\013')p 2792 5249 V 2829 5340 a Fv(F)2906 5306 y Ft(\024)2892 5367 y(I)3025 5272 y Fs(\024)29 b Fv(C)23 b(M)3328 5231 y Ft(\024)3390 5132 y Fp(\022)3464 5205 y Fv(p)f Fw(+)g Fv(q)3547 5340 y(p)3680 5132 y Fp(\023)3753 5272 y Fv(:)35 5545 y Fw(W)-8 b(e)33 b(deduce)i(that)d Fv(\013)803 5464 y Fp(\000)816 5545 y Fh(G)933 5575 y Ft(p;q)1026 5464 y Fp(\001)1100 5545 y Fs(\025)c Fw(1.)p eop %%Page: 11 11 11 10 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h(GRASSMANN)d(MANIF)n(OLD)760 b Fk(11)35 619 y Fu(3.3.3.)49 b(Upp)-5 b(er)43 b(b)-5 b(ound)42 b(of)h Fv(\013)q Fw(\()-33 b Fh(G)1216 650 y Ft(p;q)1310 619 y Fw(\).)42 b(|)64 b(W)-8 b(e)42 b(use)g(here)f(a)g(metho)s(d)g(whic)m (h)g(can)g(b)s(e)h(found)f(in)f([)p Fx(Re)p Fw(])35 762 y(for)d(the)h(complex)e(pro)5 b(jectiv)m(e)39 b(space.)58 b(Let)37 b Fv(I)45 b Fw(in)37 b Fs(I)7 b Fw(.)58 b(W)-8 b(e)37 b(de\014ne)2535 737 y(~)2509 762 y Fv(K)44 b Fw(from)36 b Fv(M)2975 726 y Fo(\003)3015 762 y Fw(\()p Fv(p)25 b Fw(+)g Fv(q)t(;)17 b(p)p Fw(\))37 b(to)g Fq(P)3626 726 y Fr(1)3667 762 y Fw(\()p Fq(R)5 b Fw(\))35 902 y(b)m(y)37 b(the)f(relation)732 877 y(~)706 902 y Fv(K)7 b Fw(\()p Fv(M)j Fw(\))34 b(=)1119 821 y Fp(\002)1177 902 y Fs(j)17 b Fw(det)33 b Fv(m)1475 928 y Fe(I)1515 902 y Fw(\()p Fv(H)8 b Fw(\))17 b Fs(j)1725 866 y Fr(2)1763 902 y Fv(;)g Fw(det)1976 866 y Ft(t)1989 902 y Fv(M)p 2093 822 89 4 v -7 w(M)2198 821 y Fp(\003)2240 902 y Fw(.)2346 877 y(~)2320 902 y Fv(K)43 b Fw(is)35 b(in)m(v)-5 b(arian)m(t)34 b(b)m(y)j(the)f(action)f(of)g(the)35 1041 y(structural)30 b(group)g Fv(G)834 1056 y Ft(p)873 1041 y Fw(\()p Fq(C)37 b Fw(\),)f(so)30 b(it)f(induces)i(a)e Fv(C)1807 1005 y Fo(1)1912 1041 y Fw(map)g Fv(K)37 b Fw(from)28 b Fv(G)2550 1056 y Ft(p;q)2643 1041 y Fw(\()p Fq(C)37 b Fw(\))f(to)29 b Fq(P)3013 1005 y Fr(1)3054 1041 y Fw(\()p Fq(R)5 b Fw(\).)49 b(Remark)29 b(that)35 1181 y Fv( )j Fw(=)c(log)16 b Fv(K)40 b Fw(is)32 b(a)g(K\177)-49 b(ahler)32 b(p)s(oten)m(tial)f(on) h Fv(U)1611 1196 y Ft(I)1684 1181 y Fw(for)g(the)h(metric)p Fh(G)2390 1211 y Ft(p;q)2483 1181 y Fw(.)35 1378 y Fi(Lemma)39 b(3.5)p Fw(.)k(|)48 b Fu(Ther)-5 b(e)34 b(exists)h(a)g(de)-5 b(cr)g(e)g(asing)33 b(se)-5 b(quenc)g(e)2257 1298 y Fp(\000)2303 1378 y Fv(')2367 1393 y Ft(n)2414 1298 y Fp(\001)2459 1417 y Ft(n)p Fo(\025)p Fr(0)2632 1378 y Fu(of)34 b(admissible)g (functions)g(with)35 1521 y(p)-5 b(ositive)35 b(maxima)e(which)h(c)-5 b(onver)g(ges)34 b(p)-5 b(ointwise)34 b(to)h Fs(\000)p Fv( )k Fu(on)c Fv(\031)2385 1441 y Fp(\000)2430 1521 y Fv(U)2496 1536 y Ft(I)2536 1441 y Fp(\001)2582 1521 y Fu(.)35 1719 y(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(W)-8 b(e)45 b(construct)h(a)e(decreasing)h(sequence)2085 1638 y Fp(\000)2131 1719 y Fv(f)2179 1734 y Ft(n)2226 1638 y Fp(\001)2272 1758 y Ft(n)p Fo(\025)p Fr(0)2453 1719 y Fw(of)f Fv(C)2653 1683 y Fo(1)2772 1719 y Fw(con)m(v)m(ex)j (functions)e(on)f Fq(R)3750 1734 y Fr(+)35 1862 y Fw(satisfying)32 b(the)g(conditions)g(1)21 b(+)h Fv(f)1331 1826 y Fo(0)1320 1887 y Ft(n)1394 1862 y Fv(>)28 b Fw(0,)k Fv(f)1654 1877 y Ft(n)1701 1862 y Fw(\()p Fv(x)p Fw(\))c(=)g Fs(\000)2041 1782 y Fp(\000)2087 1862 y Fw(1)21 b Fs(\000)h Fw(1)p Fv(=n)2412 1782 y Fp(\001)2458 1862 y Fv(x)32 b Fw(for)g Fv(x)h Fw(in)e([0)p Fv(;)17 b(n)p Fw(])32 b(and)h Fv(f)3370 1877 y Ft(n)3417 1862 y Fw(\()p Fv(x)p Fw(\))28 b(=)f Fs(\000)p Fv(n)35 2002 y Fw(for)j Fv(x)e Fs(\025)g Fw(2)p Fv(n)p Fw(.)43 b(Let)31 b Fv(y)i Fw(b)s(e)d(an)h(elemen)m(t)f(of)f Fv(\031)t Fw(\()p Fv(U)1694 2017 y Ft(I)1734 2002 y Fw(\))1772 1966 y Ft(c)1837 2002 y Fw(and)i(\012)2095 2017 y Ft(n)2172 2002 y Fw(the)g(set)g(of)f(the)h(elemen)m(ts)f Fv(x)h Fw(in)e Fv(\031)t Fw(\()p Fv(U)3519 2017 y Ft(I)3559 2002 y Fw(\))h(suc)m(h)35 2141 y(that)38 b Fv( )t Fw(\()p Fv(x)p Fw(\))e Fv(>)f Fw(2)p Fv(n)p Fw(.)58 b(Since)37 b Fv(F)1111 2156 y Ft(I)1151 2141 y Fw(\()p Fv(y)t Fw(\))e(=)h([0)p Fv(;)17 b Fw(1],)38 b(there)g(exists)g(a)f(neigh)m(b)s(orho)s(o)s(d)f Fv(V)59 b Fw(of)37 b(y)h(suc)m(h)g(that)f(the)35 2281 y(inequalit)m(y)28 b Fv(z)k(>)c(e)710 2245 y Fr(2)p Ft(n)821 2281 y Fw(holds)g(for)f(ev)m(ery)k(p)s(oin)m(t)c([1)p Fv(;)17 b(z)t Fw(])29 b(in)f Fv(F)2118 2296 y Ft(I)2158 2281 y Fw(\()p Fv(V)21 b Fw(\).)42 b(Th)m(us)30 b Fv(V)35 b Fs(\\)14 b Fv(\031)2855 2200 y Fp(\000)2901 2281 y Fv(U)2967 2296 y Ft(I)3007 2200 y Fp(\001)3081 2281 y Fw(is)28 b(included)g(in)f(\012)3740 2296 y Ft(n)3788 2281 y Fw(.)35 2420 y(W)-8 b(e)33 b(ha)m(v)m(e)h(pro)m(v)m(ed)g(that)e Fv(W)1048 2435 y Ft(n)1122 2420 y Fw(=)c(\012)1296 2435 y Ft(n)1365 2420 y Fs([)22 b Fv(\031)1512 2339 y Fp(\000)1557 2420 y Fv(U)1623 2435 y Ft(I)1664 2339 y Fp(\001)1709 2362 y Ft(c)1744 2420 y Fw(,)32 b(so)h(that)f Fv(W)2226 2435 y Ft(n)2305 2420 y Fw(is)g(an)g(op)s(en)h(neigh)m(b)s(orho)s(o)s (d)e(of)h Fv(\031)3556 2339 y Fp(\000)3601 2420 y Fv(U)3667 2435 y Ft(I)3707 2339 y Fp(\001)3753 2362 y Ft(c)3788 2420 y Fw(.)35 2560 y(W)-8 b(e)32 b(de\014ne)g Fv(')546 2575 y Ft(n)624 2560 y Fw(b)m(y)g Fv(')822 2575 y Ft(n)897 2560 y Fw(=)27 b Fv(f)1048 2575 y Ft(n)1114 2560 y Fs(\016)19 b Fv( )35 b Fw(on)c Fv(\031)1474 2479 y Fp(\000)1520 2560 y Fv(U)1586 2575 y Ft(I)1626 2479 y Fp(\001)1703 2560 y Fw(and)g Fv(')1955 2575 y Ft(n)2030 2560 y Fw(=)c Fs(\000)p Fv(n)32 b Fw(on)f Fv(W)2526 2575 y Ft(n)2573 2560 y Fw(.)43 b(Th)m(us)32 b Fv(')2952 2575 y Ft(n)3030 2560 y Fw(is)f(w)m(ell)f(de\014ned)j(and)35 2699 y Fv(')99 2714 y Ft(n)146 2699 y Fw(\(0\))28 b(=)f(0.)43 b(It)33 b(remains)f(to)g(sho)m(w)i(that)e Fv(')1627 2714 y Ft(n)1706 2699 y Fw(is)g(admissible)f(on)i Fv(\031)2472 2618 y Fp(\000)2517 2699 y Fv(U)2583 2714 y Ft(I)2623 2618 y Fp(\001)2669 2699 y Fw(.)43 b(W)-8 b(e)33 b(ha)m(v)m(e)187 2795 y Fp(\020)214 2906 y Fh(G)331 2936 y Ft(p;q)446 2906 y Fw(+)22 b Fv(i)17 b(@)p 650 2825 57 4 v 5 w(@)24 b(')789 2921 y Ft(n)836 2795 y Fp(\021)895 2975 y Ft(\025)p 948 2937 31 3 v(\026)1011 2906 y Fw(=)j Fv(@)1165 2921 y Ft(\025)p 1219 2883 V 1 w(\026)1253 2906 y Fv( )g Fw(+)22 b Fv(@)1492 2921 y Ft(\025)1537 2825 y Fp(\000)1583 2906 y Fv(f)1642 2865 y Fo(0)1631 2930 y Ft(n)1700 2906 y Fs(\016)g Fv( )1839 2825 y Fp(\001)1885 2906 y Fv(@)p 1936 2883 35 3 v 1924 2921 a Ft(\026)1971 2906 y Fv( )32 b Fw(=)2169 2825 y Fp(\000)2215 2906 y Fw(1)22 b(+)g Fv(f)2443 2865 y Fo(0)2432 2930 y Ft(n)2501 2906 y Fs(\016)g Fv( )2640 2825 y Fp(\001)2686 2906 y Fv(@)2737 2921 y Ft(\025)p 2790 2883 31 3 v(\026)2825 2906 y Fv( )k Fw(+)c Fv(f)3071 2865 y Fo(00)3060 2930 y Ft(n)3135 2906 y Fs(\016)g Fv( )f(@)3342 2921 y Ft(\025)3388 2906 y Fv( )f(@)p 3534 2883 V 15 x Ft(\026)3570 2906 y Fv( )t(:)35 3134 y Fw(Hence)39 b(the)f(matrix)d(of)i(the)h(metric)5 b Fh(G)1506 3164 y Ft(p;q)1624 3134 y Fw(+)25 b Fv(i)17 b(@)p 1831 3053 57 4 v 5 w(@)24 b(')1970 3149 y Ft(n)2054 3134 y Fw(is)36 b(of)h(the)h(form)e Fv(A)25 b Fw(+)g Fv(T)51 b Fw(where)39 b Fv(A)e Fw(is)g(p)s(ositiv)m(e)35 3273 y(de\014nite)e(and)f Fv(T)48 b Fw(has)34 b(rank)g(one)h(and)f(p)s(ositiv)m(e)f(trace.)48 b(So)34 b Fv(A)24 b Fw(+)f Fv(T)47 b Fw(is)34 b(p)s(ositiv)m(e)f (de\014nite)i(and)f(w)m(e)h(get)35 3413 y(the)e(result.)p 3744 3413 4 66 v 3748 3350 59 4 v 3748 3413 V 3806 3413 4 66 v 35 3610 a Fi(Lemma)39 b(3.6)p Fw(.)k(|)48 b Fu(L)-5 b(et)35 b Fv(n)g Fu(in)g Fq(N)1212 3574 y Fo(\003)1292 3610 y Fu(and)f Fv(r)k Fu(a)d(p)-5 b(ositive)34 b(r)-5 b(e)g(al)34 b(numb)-5 b(er.)45 b(Then)1325 3693 y Fp(Z)1380 3919 y Fo(jj)p Ft(X)5 b Fo(jj\024)p Ft(r)1642 3762 y Fv(dV)1750 3777 y Ft(X)1816 3762 y Fw(\()p Fv(M)1948 3777 y Ft(n)1996 3762 y Fw(\()p Fq(C)20 b Fw(\)\))p 1642 3806 540 4 v 1738 3834 a Fp(\014)1738 3894 y(\014)1771 3919 y Fw(det)d Fv(X)2012 3834 y Fp(\014)2012 3894 y(\014)2045 3861 y Fr(2)2219 3829 y Fw(=)28 b(+)p Fs(1)p Fv(:)35 4090 y Fu(Pr)-5 b(o)g(of)p Fw(.)43 b(|)e(W)-8 b(e)33 b(can)g(write)683 4194 y Fp(Z)738 4419 y Fo(jj)p Ft(X)5 b Fo(jj\024)p Ft(r)999 4262 y Fv(dV)1107 4277 y Ft(X)1174 4262 y Fw(\()p Fv(M)1306 4277 y Ft(n)1353 4262 y Fw(\()p Fq(C)20 b Fw(\)\))p 999 4306 V 1096 4335 a Fp(\014)1096 4395 y(\014)1129 4419 y Fw(det)d Fv(X)1370 4335 y Fp(\014)1370 4395 y(\014)1403 4361 y Fr(2)1577 4329 y Fw(=)1717 4205 y Fo(1)1680 4235 y Fp(X)1688 4447 y Ft(k)r Fr(=0)1891 4194 y Fp(Z)1946 4419 y Ft(r)r(=)p Fr(2)2050 4400 y Fe(k)q Fg(+1)2165 4419 y Fo(\024jj)p Ft(X)5 b Fo(jj\024)p Ft(r)r(=)p Fr(2)2522 4400 y Fe(k)2590 4262 y Fv(dV)2698 4277 y Ft(X)2765 4262 y Fw(\()p Fv(M)2897 4277 y Ft(n)2944 4262 y Fw(\()p Fq(C)20 b Fw(\)\))p 2590 4306 V 2687 4335 a Fp(\014)2687 4395 y(\014)2720 4419 y Fw(det)d Fv(X)2961 4335 y Fp(\014)2961 4395 y(\014)2994 4361 y Fr(2)3140 4329 y Fs(\001)35 4596 y Fw(W)-8 b(e)33 b(put)g Fv(Y)49 b Fw(=)28 b(2)641 4560 y Ft(k)683 4596 y Fv(X)8 b Fw(,)33 b(so)713 4679 y Fp(Z)769 4905 y Ft(r)r(=)p Fr(2)873 4886 y Fe(k)q Fg(+1)988 4905 y Fo(\024jj)p Ft(X)5 b Fo(jj\024)p Ft(r)r(=)p Fr(2)1345 4886 y Fe(k)1413 4747 y Fv(dV)1521 4762 y Ft(X)1588 4747 y Fw(\()p Fv(M)1720 4762 y Ft(n)1767 4747 y Fw(\()p Fq(C)20 b Fw(\)\))p 1413 4792 V 1510 4820 a Fp(\014)1510 4880 y(\014)1543 4905 y Fw(det)d Fv(X)1784 4820 y Fp(\014)1784 4880 y(\014)1817 4847 y Fr(2)1990 4815 y Fw(=)2094 4679 y Fp(Z)2149 4905 y Fr(1)p Ft(=)p Fr(2)p Fo(\024jj)p Ft(Y)f Fo(jj\024)p Fr(1)2566 4747 y Fv(dV)2674 4762 y Ft(Y)2734 4747 y Fw(\()p Fv(M)2866 4762 y Ft(n)2914 4747 y Fw(\()p Fq(C)j Fw(\)\))p 2566 4792 534 4 v 2665 4820 a Fp(\014)2665 4880 y(\014)2698 4905 y Fw(det)e Fv(Y)2928 4820 y Fp(\014)2928 4880 y(\014)2961 4847 y Fr(2)3109 4815 y Fs(\001)35 5066 y Fw(The)37 b(terms)e(in)g(the)g(series)h(are)g(strictly)e(p)s(ositiv)m (e)h(and)h(indep)s(enden)m(t)g(of)f Fv(k)s Fw(.)52 b(The)36 b(sum)f(is)g(therefore)35 5206 y(in\014nite.)p 3744 5206 4 66 v 3748 5143 59 4 v 3748 5206 V 3806 5206 4 66 v eop %%Page: 12 12 12 11 bop 35 283 a Fk(12)1446 b Fj(JULIEN)32 b(GRIV)-9 b(A)n(UX)35 619 y Fw(W)h(e)46 b(can)f(no)m(w)h(pro)m(v)m(e)g(that)e Fv(\013)1184 539 y Fp(\000)1197 619 y Fh(G)1315 650 y Ft(p;q)1408 539 y Fp(\001)1498 619 y Fw(is)h(upp)s(er)g(b)s(ounded)h(b) m(y)g(1.)80 b(Supp)s(ose)46 b(that)f Fv(\013)3297 539 y Fp(\000)3310 619 y Fh(G)3427 650 y Ft(p;q)3520 539 y Fp(\001)3615 619 y Fv(>)j Fw(1.)35 807 y(Then)i(there)g(exists)f(a)g (p)s(ositiv)m(e)f Fv(C)56 b Fw(suc)m(h)50 b(that)f(for)f(ev)m(ery)i(in) m(teger)f Fv(n)p Fw(,)2837 671 y Fp(Z)2893 896 y Ft(\031)r Fr(\()p Ft(U)3011 907 y Fe(I)3046 896 y Fr(\))3094 807 y Fv(e)3139 765 y Fo(\000)p Ft(')3240 773 y Fe(n)3342 807 y Fs(\024)56 b Fv(C)7 b Fw(.)92 b(Us-)35 1057 y(ing)44 b(Lemma)e(\(3.5\))i(and)g(monotonous)g(con)m(v)m(ergence,)2156 921 y Fp(Z)2211 1147 y Ft(\031)r Fr(\()p Ft(U)2329 1158 y Fe(I)2364 1147 y Fr(\))2412 1057 y Fv(F)2475 1072 y Ft(I)2563 1057 y Fs(\024)k Fv(C)7 b Fw(.)78 b(Since)44 b Fv(\031)t Fw(\()p Fv(U)3299 1072 y Ft(I)3339 1057 y Fw(\))3377 1021 y Ft(c)3456 1057 y Fw(has)h(zero)35 1307 y(measure,)459 1172 y Fp(Z)514 1397 y Ft(G)569 1405 y Fe(p;q)654 1397 y Fr(\()p Fa(C)27 b Fr(\))790 1307 y Fv(F)853 1322 y Ft(I)942 1307 y Fs(\024)50 b Fv(C)7 b Fw(.)83 b(Let)1455 1282 y(~)1443 1307 y Fv(I)54 b Fw(in)44 b Fs(I)53 b Fw(b)s(e)46 b(suc)m(h)h(that)e Fv(I)39 b Fs(\\)2567 1282 y Fw(~)2555 1307 y Fv(I)58 b Fw(=)49 b Fs(;)d Fw(\(this)f(is)g(p)s(ossible)f(since)35 1525 y Fv(p)62 b Fs(\024)f Fv(q)t Fw(\).)103 b(W)-8 b(e)53 b(ha)m(v)m(e)g Fv(P)1002 1535 y Fr(~)994 1552 y Ft(I)1034 1444 y Fp(\010)1092 1525 y Fv(m)1177 1540 y Ft(I)1234 1444 y Fp(\000)1280 1525 y Fv(P)1351 1535 y Fr(~)1343 1552 y Ft(I)1383 1444 y Fp(\001)o(\011)1486 1466 y Fo(\000)p Fr(1)1642 1525 y Fw(=)61 b Fv(P)1842 1540 y Ft(I)1882 1525 y Fw(.)103 b(Remark)51 b(that)i Fv(m)2715 1540 y Ft(I)2755 1444 y Fp(\000)2800 1525 y Fv(P)2871 1535 y Fr(~)2863 1552 y Ft(I)2903 1444 y Fp(\001)3010 1525 y Fw(=)61 b Fv(m)3232 1540 y Ft(I)3273 1444 y Fp(\000)3318 1525 y Fv(Z)3393 1535 y Fr(~)3385 1552 y Ft(I)3425 1444 y Fp(\001)3471 1525 y Fw(.)102 b(Th)m(us)35 1669 y(det)171 1589 y Fp(\000)217 1669 y Fv(I)8 b(d)25 b Fw(+)420 1633 y Ft(t)458 1669 y Fv(Z)525 1684 y Ft(I)p 582 1589 58 4 v 565 1669 a Fv(Z)639 1684 y Ft(I)679 1589 y Fp(\001)761 1669 y Fw(=)36 b(det)1009 1589 y Fp(\000)1054 1611 y Ft(t)1067 1669 y Fv(P)1138 1679 y Fr(~)1130 1696 y Ft(I)p 1187 1589 60 4 v 1170 1669 a Fv(P)1255 1679 y Fr(~)1247 1696 y Ft(I)1287 1589 y Fp(\001)1349 1585 y(\014)1349 1644 y(\014)1382 1669 y Fw(det)17 b Fv(m)1619 1684 y Ft(I)1659 1589 y Fp(\000)1705 1669 y Fv(Z)1780 1679 y Fr(~)1772 1696 y Ft(I)1812 1589 y Fp(\001)1857 1585 y(\014)1857 1644 y(\014)1891 1611 y Fo(\000)p Fr(2)1985 1669 y Fw(.)59 b(F)-8 b(or)2251 1585 y Fp(\015)2251 1644 y(\015)2306 1669 y Fv(Z)2381 1679 y Fr(~)2373 1696 y Ft(I)2413 1585 y Fp(\015)2413 1644 y(\015)2504 1669 y Fs(\024)37 b Fv(r)s Fw(,)i(det)2867 1589 y Fp(\000)2912 1611 y Ft(t)2925 1669 y Fv(P)2996 1679 y Fr(~)2988 1696 y Ft(I)p 3045 1589 V 3028 1669 a Fv(P)3113 1679 y Fr(~)3105 1696 y Ft(I)3144 1589 y Fp(\001)3227 1669 y Fs(\024)d Fv(M)10 b Fw(,)40 b(so)e(that)35 1729 y Fp(Z)91 1954 y Fo(jj)p Ft(Z)186 1965 y Fg(~)179 1978 y Fe(I)213 1954 y Fo(jj\024)p Ft(r)372 1787 y Fv(dV)480 1802 y Ft(Z)535 1813 y Fg(~)528 1826 y Fe(I)567 1787 y Fw(\()p Fv(M)699 1802 y Ft(q)r(;p)792 1787 y Fw(\()p Fq(C)f Fw(\)\))p 372 1841 623 4 v 392 1870 a Fp(\014)392 1930 y(\014)426 1955 y Fw(det)17 b Fv(m)663 1970 y Ft(I)703 1874 y Fp(\000)749 1955 y Fv(Z)824 1965 y Fr(~)816 1982 y Ft(I)855 1874 y Fp(\001)901 1870 y(\014)901 1930 y(\014)934 1896 y Fr(2)1032 1864 y Fv(<)28 b Fw(+)p Fs(1)p Fw(.)39 b(In)m(tegrating)23 b(o)m(v)m(er)i(the)f (remaining)d(v)-5 b(ariables)3073 1784 y Fp(\000)3119 1864 y Fv(Z)3186 1879 y Ft(ij)3246 1784 y Fp(\001)3292 1903 y Ft(i)p Fo(2)3369 1887 y Fd(e)3363 1903 y Ft(I)3399 1884 y Fe(c)3431 1903 y Fo(\\)p Ft(I)3514 1884 y Fe(c)3573 1864 y Fw(yields)35 2004 y Fp(Z)91 2230 y Fo(jj)p Ft(Z)5 b Fo(jj\024)p Ft(r)341 2072 y Fv(dV)449 2087 y Ft(Z)505 2072 y Fw(\()p Fv(M)637 2087 y Ft(p)677 2072 y Fw(\()p Fq(C)20 b Fw(\)\))p 341 2117 522 4 v 436 2145 a Fp(\014)436 2205 y(\014)469 2230 y Fw(det)d Fv(Z)695 2145 y Fp(\014)695 2205 y(\014)729 2172 y Fr(2)918 2140 y Fv(<)46 b Fw(+)p Fs(1)p Fw(,)f(whic)m(h)f(is)e(in)g(con)m(tradiction)g(with)h(the)g (result)g(of)g(Lemma)e(\(3.6\).)35 2358 y(Th)m(us)35 b(w)m(e)e(obtain)f Fv(\013)793 2277 y Fp(\000)806 2358 y Fh(G)923 2388 y Ft(p;q)1016 2277 y Fp(\001)1089 2358 y Fs(\024)d Fw(1.)1663 2672 y Fx(References)35 2869 y Fw([Au1])117 b Fi(T.)41 b(A)m(ubin)p Fw(,)898 2844 y Fu(\023)884 2869 y(Equations)c(du)h(typ)-5 b(e)38 b(Monge-A)n(mp)n (\022)-47 b(er)-5 b(e)35 b(sur)i(les)g(vari)n(\023)-47 b(et)n(\023)g(es)35 b(k\177)-50 b(ahl)n(\023)j(eriennes)35 b(c)-5 b(om-)382 3009 y(p)g(actes)p Fw(,)32 b(Bull.)g(Sci.)g(Math.)h Fx(102)f Fw(\(1978\),)g(63-95.)35 3158 y([Au2])117 b Fi(T.)40 b(A)m(ubin)p Fw(,)34 b Fu(R)n(\023)-47 b(e)-5 b(duction)35 b(du)i(c)-5 b(as)36 b(p)-5 b(ositif)35 b(de)h(l')n(\023) -47 b(equation)35 b(de)h(Monge-A)n(mp)n(\022)-47 b(er)-5 b(e)34 b(sur)i(les)g(var-)382 3298 y(i)n(\023)-47 b(et)n(\023)g(es)33 b(K\177)-50 b(ahl)n(\023)j(eriennes)32 b(c)-5 b(omp)g(actes)34 b(\022)-50 b(a)35 b(la)g(d)n(\023)-47 b(emonstr)-5 b(ation)32 b(d'une)j(in)n(\023)-47 b(e)-5 b(galit)n(\023)-47 b(e)p Fw(,)30 b(J.)j(F)-8 b(unct.)33 b(Anal.)382 3437 y Fx(57)g Fw(\(1984\),)e(143-153.)35 3586 y([Au3])117 b Fi(T.)42 b(A)m(ubin)p Fw(,)c Fu(M)n(\023)-47 b(etriques)37 b(d'Einstein-K\177) -50 b(ahler)37 b(et)h(exp)-5 b(onentiel)37 b(de)h(fonctions)g (admissibles)p Fw(,)382 3726 y(J.)33 b(F)-8 b(unc.)33 b(Anal.)f Fx(88)g Fw(\(1990\),)g(385-394.)35 3875 y([Au4])117 b Fi(T.)29 b(A)m(ubin)p Fw(,)c Fu(Some)h(Non-line)-5 b(ar)26 b(Pr)-5 b(oblems)26 b(in)g(R)n(iemannian)f(Ge)-5 b(ometry)p Fw(,)26 b(Springer-V)-8 b(erlag,)382 4015 y(Berlin,)32 b(1998.)35 4164 y([Be1])132 b Fi(A.)35 b(Ben)g(Abdesselem) p Fw(,)29 b Fu(L)-5 b(ower)32 b(b)-5 b(ound)32 b(of)g(admissible)f (functions)i(on)f(spher)-5 b(e)p Fw(,)30 b(Bull.)e(Sci.)382 4304 y(Math)33 b Fx(126)g Fw(\(2002\),)e(675-680.)35 4453 y([Be2])132 b Fi(A.)69 b(Ben)f(Abdesselem)p Fw(,)g Fu(Envelopp)-5 b(es)60 b(inf)n(\023)-47 b(erieur)-5 b(es)60 b(de)h(fonctions)g(admissibles)f(sur)382 4592 y(l'esp)-5 b(ac)g(e)46 b(pr)-5 b(oje)g(ctif)47 b(c)-5 b(omplexe.)46 b(Cas)g(sym)n(\023)-47 b(etrique)p Fw(,)49 b(T)-8 b(o)46 b(app)s(ear)g(in)f(Di\013.)f(Geom.)h(and)h(its)382 4732 y(App.)35 4881 y([Be-Ch1])k Fi(A.)44 b(Ben)g(Abdesselem,)g(P.)h (Cherrier)p Fw(,)40 b Fu(Einstein-K\177)-50 b(ahler)39 b(metrics)i(on)f(a)g(class)g(of)382 5021 y(bund)5 b(les)26 b(involving)f(inte)-5 b(gr)g(al)26 b(weights)p Fw(,)f(J.)f(Math.)g (Pures)h(Appl.)e Fx(3)p Fw(,)i(v)m(ol)e(81,)i(\(2002\),)g(259-281.)35 5170 y([Be-Ch2])50 b Fi(A.)40 b(Ben)g(Abdesselem,)g(P.)g(Cherrier)p Fw(,)35 b Fu(Estimations)i(of)g(R)n(ic)-5 b(ci)36 b(tensor)h(on)g(c)-5 b(ertain)382 5310 y(F)e(ano)34 b(manifolds)p Fw(,)d(Math.)i(Z.)f Fx(233)p Fw(,)h(2000,)e(481-505.)35 5459 y([F)-8 b(u])183 b Fi(A.)42 b(Fut)-7 b(aki)p Fw(,)38 b Fu(A)n(n)g(obstruction)g(to)h (the)f(existenc)-5 b(e)38 b(of)g(K\177)-50 b(ahler-Einstein)37 b(metrics)p Fw(,)g(In)m(v)m(en)m(t.)382 5598 y(Math.)c Fx(73)p Fw(,)g(1983,)f(437-443.)p eop %%Page: 13 13 13 12 bop 885 283 a Fj(TIAN'S)32 b(INV)-9 b(ARIANT)31 b(OF)i(THE)h(GRASSMANN)d(MANIF)n(OLD)760 b Fk(13)35 619 y Fw([Ko-No])48 b Fi(S.)42 b(K)m(oba)-7 b(y)g(ashi,)43 b(K.)f(Nomizu)p Fw(,)c Fu(F)-7 b(oundations)36 b(of)i(Di\013er)-5 b(ential)37 b(Ge)-5 b(ometry)p Fw(,)38 b(V)-8 b(olume)35 b(I)s(I)382 759 y(John)e(Wiley)f(\(1969\).)35 912 y([Li])204 b Fi(A.)27 b(Lichner)n(o)n(wicz)p Fw(,)e Fu(Sur)g(les)g(tr)-5 b(ansformations)25 b(analytiques)g(des)g(vari)n(\023)-47 b(et)n(\023)g(es)24 b(k\177)-50 b(ahl)n(\023)j(eriennes)p Fw(,)382 1052 y(Cr.)33 b(Acac.)h(Sci)e Fx(244)p Fw(,)g(1957,)g (3011-3014.)35 1205 y([Ma])155 b Fi(Y.)54 b(Ma)-7 b(tsushima)p Fw(,)52 b Fu(Sur)d(la)g(structur)-5 b(e)50 b(du)f(gr)-5 b(oup)g(e)48 b(d'hom)n(\023)-47 b(eomorphismes)45 b(analytiques)382 1345 y(d'une)35 b(c)-5 b(ertaine)34 b(vari)n(\023)-47 b(et)n(\023)g(e)33 b(k\177)-50 b(ahl)n(\023)j(erienne)p Fw(,)30 b(Nago)m(y)m(a)j(Math.)f(J.)h Fx(11)g Fw(\(1957\),)e(145-150.) 35 1498 y([Re])178 b Fi(C.)58 b(Real)p Fw(,)d Fu(M)n(\023)-47 b(etriques)51 b(d'Einstein-K\177)-50 b(ahler)51 b(sur)h(des)f(vari)n (\023)-47 b(et)n(\023)g(es)50 b(\022)-50 b(a)51 b(pr)-5 b(emi)n(\022)-47 b(er)-5 b(e)50 b(classe)h(de)382 1637 y(Chern)34 b(p)-5 b(ositive)p Fw(,)32 b(J.)h(F)-8 b(unc.)33 b(Anal.)f Fx(106)g Fw(\(1992\),)g(145-188.)35 1791 y([Ti])195 b Fi(G.)29 b(Tian)p Fw(,)e Fu(On)g(K\177)-50 b(ahler-Einstein)26 b(metrics)h(on)g(c)-5 b(ertain)27 b(K\177)-50 b(ahler)27 b(manifolds)f(with)h Fv(C)3491 1755 y Fr(1)3531 1791 y Fw(\()p Fv(M)10 b Fw(\))28 b Fv(>)382 1930 y Fw(0,)33 b(In)m(v)m(en)m(t.)i(Math.)d Fx(89)h Fw(\(1987\),)f(225-246.)35 2084 y([Y)-8 b(a])179 b Fi(S.)30 b(T.)h(Y)-9 b(a)n(u)p Fw(,)27 b Fu(On)h(the)h(R)n(ic)-5 b(ci)28 b(curvatur)-5 b(e)29 b(of)f(a)h(c)-5 b(omp)g(act)27 b(K\177)-50 b(ahler)28 b(manifold)g(and)g(the)g(c)-5 b(omplex)382 2223 y(Monge-A)n(mp)n(\022) -47 b(er)-5 b(e)33 b(e)-5 b(quations)p Fw(,)32 b(I.)h(Comm.)e(Pure)j (Appl.)e(Math.)h Fx(31)f Fw(\(1978\),)g(339-411.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF  ---------------0512111607496--