Riemann Surfaces by way of Analytic Geometry by D. Varolin, AMS 2011.
An introduction to Analysis on (mainly compact) Riemann surfaces. In complex analysis one studies analytic functions-- their zeros, growth and mapping properties. There are no holomorphic functions on compact Riemann surfaces. Instead one has twisted holomorphic functions-- namely, holomorphic sections of line bundles and meromorphic functions. We will concentrate on holomorphic line bundles, their holomorphic sections, and Hermitian metrics on line bundles and their curvature forms. The topics will include: the uniformization theorem, HormanderŐs theorem, Mittage-Leffler problem, KodairaŐs Embedding theorem and Riemann-Roch theorem.
Office Location: Krieger Hall Rm 220
Office Hours: W 3:00-5:00
MW 12:00-1:15 at Charles Commons 324