Math 244, Spring 2008 - Riemann surfaces and algebraic curves

Dragos Oprea, MWF 10-10:50, 381 T

Topics to be covered:

1. Complex manifolds. Riemann surfaces. Basic definitions. Examples.

2. Sheaves and their cohomology. Cech cohomology. Dolbeault cohomology.

3. Divisors and line bundles. Linear systems and projective embeddings.

4. The Riemann-Roch theorem and applications.

5. Serre duality.

6. Riemann-Hurwitz formula.

7. Curves of low genus.

8. The Jacobian. The Abel-Jacobi map.

9. An introduction to the moduli space of curves.

Prerequisities: Basic complex analysis. Some differential geometry and some algebraic geometry are useful, but not formally required. The best approach to see if you have the prerequisites is to attend the first few lectures.

Lecture Summaries