Moduli spaces in algebraic geometry (259x)
SyllabusFull notes (Under construction)
Lectures
1. Overview
2. Moduli functors and Grassmannians
3. Grassmannians (cont.) and flat morphisms
4. Flat morphisms and Hilbert polynomials
5. Base change, the Hilbert functor
6. The Hilbert and Quot schemes
7. The Hilbert and Quot Schemes (cont.)
8. Hom schemes, CM regularity
9. CM regularity, flattening stratifications
10. Flattening stratifications, functoriality properties of Hilb and Quot
11. Weil restriction, quasi-projective schemes
12. The Picard functor
13. Relative effective cartier divisors
14. The Abel-Jacobi map
15-16. The Abel-Jacobi map (cont.), boundedness, quotients by equivalence relations
17-18. Sheaves, quotients, representability of the Picard functor
19-21. Deformation theory of line bundles, compactified Jacobians of integral curves
22. The Hilbert scheme of points on surfaces
23-24. The moduli of curves
Homework
Problem set 1. Due October 7.
Problem set 2. Due November 6.