Mathematics 272: Riemann Surfaces (Fall 2003)
Instructor:
Dick Hain
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:
- Forster, Otto, Lectures on Riemann surfaces, Graduate Texts in
Mathematics,
81. Springer-Verlag, New York, 1991.
Other references:
- Clemens, C. Herbert, A scrapbook of complex curve
theory. Second edition.
Graduate Studies in Mathematics, 55. American Mathematical Society,
Providence, RI, 2003.
- Griffiths, Phillip A., Introduction to algebraic
curves. Translated from
the Chinese by Kuniko Weltin. Translations of Mathematical Monographs, 76.
American Mathematical Society, Providence, RI, 1989.
- Gunning, R. C., Lectures on Riemann surfaces. Princeton
Mathematical Notes
Princeton University Press, Princeton, N.J. 1966.
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