Mathematics 272: Riemann Surfaces (Fall 2002)
Instructor:
Ilia Zharkov
Description:
Riemann surfaces as algebraic curves, Riemann-Hurwitz
formula, line bundles and divisors, sheaves and cohomology, Serre
duality and Kodaira vanishing theorem, linear
systems, projective embeddings, Riemann-Roch formula. Abel-Jacobi map,
special linear systems. Complex tori, abelian varieties, theta
functions, Jacobians of curves.
This course (together with Math 252) is a prerequisite for Math 273,
Algebraic Geometry.
Prerequisites:
Complex Analysis (such as Math 245) and some basic Algebraic Topology (such
as Math 261), or consent of the instructor
Text:
Principles of algebraic geometry, by Griffiths and Harris
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Duke University
Last modified: 16 March 2002