Riemann Surfaces
Seiten
1992
|
2nd Revised edition
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
978-3-540-97703-2 (ISBN)
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
978-3-540-97703-2 (ISBN)
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Covers Riemann surface theory from elementary aspects to recent research. Open and closed surfaces are treated with emphasis on the compact case and basic tools are developed to describe the analytic, geometric and algebraic properties of Riemann surfaces and their Abelian varieties.
This text covers Riemann surface theory from elementary aspects to the frontiers 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 varieties 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 Reimann vanishing theorem. A complete treatment of the uniformization of Riemann surfaces 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.
This text covers Riemann surface theory from elementary aspects to the frontiers 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 varieties 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 Reimann vanishing theorem. A complete treatment of the uniformization of Riemann surfaces 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.
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.
| Erscheint lt. Verlag | 31.1.1992 |
|---|---|
| Reihe/Serie | Graduate Texts in Mathematics ; v. 71 |
| Zusatzinfo | 27figs. |
| Verlagsort | Berlin |
| Sprache | englisch |
| Maße | 138 x 216 mm |
| Gewicht | 700 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 3-540-97703-1 / 3540977031 |
| ISBN-13 | 978-3-540-97703-2 / 9783540977032 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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