Mathematics 721 - Riemann Surfaces

This course introduces Riemann surfaces from the points of view of 1-dimensional complex manifolds and also 2-dimensional real oriented conformal manifolds. Topics covered included the structure of holomorphic maps between Riemann Surfaces (Riemann-Hurwitz Theorem), holomorphic line;vector bundles, Chern classes, the Picard group of holomorphic line bundles, the Abel-Jacobi map, and the basic theorems of Riemann Surface theory: Mittag-Leffler, Riemann-Roch, Serre duality, Kodaira embedding and Serre's GAGA principle.