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.
- ISBN13 9780387977034
- Publish Date 23 December 1991 (first published 23 September 1980)
- Publish Status Active
- Publish Country US
- Imprint Springer-Verlag New York Inc.
- Edition 2nd ed. 1992
- Format Hardcover
- Pages 366
- Language English