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More About This Textbook
Overview
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.
Editorial Reviews
Booknews
A textbook for a course for graduate students of pure mathematics and physics. Covers Riemann surfaces from the elementary aspects to recent research, emphasizing the compact case. Slightly corrected and updated from the 1979 first edition. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
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Table of Contents
0: An Overview. 1: Riemann Surfaces. 2: Existence Theorems. 3: Compact Riemann Surfaces. 4: Uniformization. 5: Automorphisms of Compact Surfaces—Elementary Theory. 6: Theta Functions. 7: Examples.