Cornell Math - MATH 712, Spring 1999

MATH 712 — Spring 1999
Seminar in Analysis

Instructor: Cliff Earle

Time:  TR 1:25-2:40

Room: WE 324

This will be an introductory course about compact Riemann surfaces and their Jacobi varieties. Complex function theory at the level of Math 612 is a prerequisite, but no previous acquaintance with Riemann surfaces will be assumed. I hope to cover the following topics, more or less along the lines of R. Narasimhan's book "Compact Riemann Surfaces."

(a) (complex) line bundles on Riemann surfaces,

(b) the first cohomology groups of various sheaves on compact Riemann surfaces,

(c) the Riemann-Roch theorem and some of its consequences,

(d) Abel's theorem, the Jacobi variety, and the Jacobi inversion problem,

(e) line bundles on the Jacobi variety, Riemann's theta function, and some of its properties.