| Lecture 1 | Wednesday, 1-20-10 | Maps to projective space | Yuecheng |
| References: Hartshorne II.7.1 and examples, and II.7.4-II.7.8 (ample
invertible sheaves and linear systems.) If time permits, also II.7.2-II.7.3. Alternative reference: Ravi Vakil's Lecture Notes, Lecture 32 |
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| Lecture 2 | Wednesday, 1-27-10 | Blowing up | Mohammad |
| References: The second half of Hartshorne II.7 ("Proj, P(E), and Blowing Up") Hartshorne's presentation of the blow-up is really unmotivated; Ravi's Notes are better about this: Ravi's Notes, Lectures 49-50 |
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| Lecture 3 | Friday, 1-29-10 | Differentials | Orit |
| References: The first two parts of Hartshorne II.8 ("Kahler Differentials" and
"Sheaves of Differentials") Hartshorne is as usual missing a lot of motivation; Ravi's presentation is really good: Ravi's Notes, Lecture 37 Ravi's Notes, Lecture 38 |
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| Lecture 4 | Friday, 2-5-10 | Differentials II | Yuan |
| References: More of Hartshorne II.8, starting with II.8.13.
The section on "Nonsingular Varieties". Also II.8.20 and the examples. See also Ravi's Notes, Lectures 39-40 |
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| Lecture 5 | Wednesday, 2-10-10 | Derived Functors and Homological Algebra | Keenan |
| Hartshorne III.1, plus your favorite homological algebra reference. |
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| Lecture 6 | Friday, 2-12-10 | Sheaf Cohomology | Keenan |
| Hartshorne III.2. |
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| Lecture 7 | Monday, 2-15-10 | Cohomology of affine schemes | Travis |
| Hartshorne III.3. |
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| Lecture 8 | Wednesday, 2-17-10 | Cech Cohomology | Yuecheng |
| Hartshorne III.4. |
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| Lecture 9 | Monday, 2-22-10 | Cohomology of Projective Space | Yuan |
| Hartshorne III.5. |
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| Lecture 10 | Wednesday, 2-24-10 | Serre Duality | Mohammad |
| Hartshorne III.7, IV.1 (From III.7, just give 7.1 and the statement of Serre Duality: Corollary 7.7,
and mention that for nonsingular varieties the dualizing sheaf is the canonical bundle.) |
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| Lecture 11 | Monday, 3-1-10 | Riemann-Roch | Mohammad |
| Hartshorne IV.1 |
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| Lecture 12 | Wednesday, 3-3-10 | Flat Families | Yuan |
| Hartshorne III.9. |
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| Lecture 13 | Monday, 3-8-10 | Grobner bases and degenerations | Keenan |
| Eisenbud, Commutative algebra with a view towards algebraic geometry,
15.8, plus background on Grobner bases from 15.1-15.3 |
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| Lecture 14 | Wednesday, 3-10-10 | Moduli Spaces | David (Helm) |
| Lecture 15 | Monday, 3-29-10 | Moduli Spaces and Deformation Theory | David (Helm) |
| Lecture 16 | Wednesday, 3-31-10 | Some fun with Hilbert schemes | David (Helm) |
| Wednesday, 4-21-10 | The Weil Conjectures | Yuecheng | |