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.
