## Moduli spaces in algebraic geometry (259x)

**Syllabus**

**Full 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.