Lectures on Riemann Surfaces:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1981
|
| Schriftenreihe: | Graduate Texts in Mathematics
81 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations. The second chapter is devoted to compact Riemann surfaces. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle. The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz' Lemma |
| Beschreibung: | 1 Online-Ressource (VIII, 256 p) |
| ISBN: | 9781461259619 9781461259633 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4612-5961-9 |
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Datensatz im Suchindex
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-5961-9 |
| format | Electronic eBook |
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| id | DE-604.BV042420440 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:06Z |
| institution | BVB |
| isbn | 9781461259619 9781461259633 |
| issn | 0072-5285 |
| language | English |
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| physical | 1 Online-Ressource (VIII, 256 p) |
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| publishDate | 1981 |
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| publisher | Springer New York |
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| series2 | Graduate Texts in Mathematics |
| spelling | Forster, Otto Verfasser aut Lectures on Riemann Surfaces by Otto Forster New York, NY Springer New York 1981 1 Online-Ressource (VIII, 256 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 81 0072-5285 This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations. The second chapter is devoted to compact Riemann surfaces. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle. The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz' Lemma Mathematics Global analysis (Mathematics) Analysis Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd rswk-swf Riemannsche Fläche (DE-588)4049991-1 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-5961-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Forster, Otto Lectures on Riemann Surfaces Mathematics Global analysis (Mathematics) Analysis Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd |
| subject_GND | (DE-588)4049991-1 |
| title | Lectures on Riemann Surfaces |
| title_auth | Lectures on Riemann Surfaces |
| title_exact_search | Lectures on Riemann Surfaces |
| title_full | Lectures on Riemann Surfaces by Otto Forster |
| title_fullStr | Lectures on Riemann Surfaces by Otto Forster |
| title_full_unstemmed | Lectures on Riemann Surfaces by Otto Forster |
| title_short | Lectures on Riemann Surfaces |
| title_sort | lectures on riemann surfaces |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik Riemannsche Fläche (DE-588)4049991-1 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik Riemannsche Fläche |
| url | https://doi.org/10.1007/978-1-4612-5961-9 |
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