Math 510. Riemann Surfaces & Algebraic Curves Lecture Syllabus
The course focuses on Riemann Surfaces from both the algebraic and function-theoretic points of view.
Topics may include:
- Holomorphic and meromorphic differential forms on Riemann surfaces
- Integration of differential forms on Riemann surfaces
- Divisors on Riemann surfaces and linear equivalence
- The genus of a compact Riemann surface
- Canonical divisors on a Riemann surface
- The Riemann-Roch theorem and applications
- Projective algebraic curves
- The canonical mapping
Possible texts:
- Forster, Lectures on Riemann surfaces
- Griffiths, Introduction to algebraic curves
- Miranda, Algebraic curves and Riemann surfaces
- Varolin, Riemann surfaces by way of analytic geometry
Effective Fall 2013. (Approved by GAC, December 2012.)