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
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.
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 | |||
23 | Nov 22 | |||
24, 25 | Nov 29, Dec 1 | |||
26, 27 | Dec 6, 8 |