3:30 pm Thursday, September 15, 2005
Geometry Seminar: Quantization of minimal resolutions of Kleinian singularities by Mitya Boyarchenko (University of Chicago) in RLM 9.166
Let X=C2/\Gamma be a Kleinian singularity, where \Gamma is a finite subgroup of SL_2(C). It is known that X admits a (unique) minimal resolution Y ---> X. We construct a family of noncommutative deformations of Y, and prove that the category of coherent sheaves on each member of the family is equivalent to the category of finitely generated modules over a corresponding noncommutative deformation of the coordinate ring C[X] of X. Our construction uses results of Holland which describe noncommutative deformations of C[X] in terms of quantum Hamiltonian reduction, the GIT construction of the minimal resolution Y of X due to Cassens-Slodowy, and the Z-algebra formalism used in a recent work of Gordon-Stafford. Submitted by
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