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.)