Riemann Surfaces /
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 var...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1992.
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| Edition: | Second edition. |
| Series: | Graduate texts in mathematics ;
71. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xvi, 366 pages) |
| ISBN: | 9781461220343 (electronic bk.) 1461220343 (electronic bk.) |
| ISSN: | 0072-5285 ; |