Riemann Surfaces

ISBN-10: 0387977031

ISBN-13: 9780387977034

Edition: 2nd 1992 (Revised)

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Description:

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. Basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the Abelian varities associated with these surfaces. 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. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject. For this new edition, the material has been brought up- to-date, and erros have been corrected. The book should be of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.
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Book details

List price: $89.95
Edition: 2nd
Copyright year: 1992
Publisher: Springer
Publication date: 12/23/1991
Binding: Hardcover
Pages: 366
Size: 6.25" wide x 9.75" long x 0.75" tall
Weight: 1.540
Language: English

An Overview
Riemann Surfaces
Existence Theorems.
Compact Riemann Surfaces
Uniformization
Automorphisms of Compact Surfaces--Elementary Theory
Theta Functions
Examples
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