Syllabus Math 510


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.)