Department of Mathematics
SUNY at Stony Brook
Deformation Theory and Moduli
Mat 626, Fall 2011
Time and Place : TueTh 12:50-2:10; Library N3085
Instructor : Radu Laza
Office : Math Tower 4-121
Email : rlaza@math.sunysb.edu
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Course Description
Prerequisite : There are no official prerequisites, but it is recommended that you have some background in Commutative Algebra, Algebraic Geometry, and Complex Geometry.
Textbook : We will not follow any particular book, but some recommendations are:
This course is an introduction to deformation theory and moduli spaces. We will start with a discussion of the basic theory (infinitesimal deformations, obstructions, Schlessinger theory) and then specialize to various deformation functors (for affine schemes, subschemes, invertible sheaves, morphisms). Finally, we will discuss Hilbert and Quot schemes and some moduli theory.
Announcements
- Welcome!
The course is open to anyone interested in algebraic geometry (esp. Moduli theory, but the material is helpful/essential in many other branches of AG).
- The content and the pace of the course will depend on the interest of the participants. It is important that you work out various examples and do the assignments.
Schedule
| Lecture |
Day |
Topic |
Chapter |
Assignments |
| 1 |
Sept 1 |
Introduction to Moduli and Deformations |
|
|
| 2, 3 |
Sept 6, 8 |
Extensions of algebras and schemes |
[S] 1.1 |
AG Ex. II.8.6 |
| 4, 5 |
Sept 13, 15 |
Locally trivial deformations of schemes |
[S] 1.2 |
AG Ex. III.9.7, 9.8, 9.9 |
| 6, 7 |
Sept 20, 22 |
Functors of Artin rings |
[S] Ch. 2 |
|
| 8 |
Sept 27 |
Functors of Artin rings |
[S] Ch. 2 |
|
| 9, 10 |
Oct 4, 6 |
|
|
|
| 11. 12 |
Oct 11, 13 |
|
|
|
| 13, 14 |
Oct 18, 20 |
|
|
|
| 15, 16 |
Oct 25, 27 |
|
|
|
| 17, 18 |
Nov 1, 3 |
|
|
|
| 19, 20 |
Nov 8, 10 |
|
|
|
| 21, 22 |
Nov 15, 17 |
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|
|
| 23 |
Nov 22 |
|
|
|
| 24, 25 |
Nov 29, Dec 1 |
|
|
|
| 26, 27 |
Dec 6, 8 |
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