| 书目名称 | Lectures on Riemann Surfaces |
| 编辑 | Otto Forster |
| 视频video | |
| 丛书名称 | Graduate Texts in Mathematics |
| 图书封面 |  |
| 描述 | 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 |
| 出版日期 | Textbook 1981 |
| 关键词 | Riemann surfaces; Riemann-roch theorem; Riemannsche Fläche; Surfaces; differential equation; minimum |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4612-5961-9 |
| isbn_softcover | 978-1-4612-5963-3 |
| isbn_ebook | 978-1-4612-5961-9Series ISSN 0072-5285 Series E-ISSN 2197-5612 |
| issn_series | 0072-5285 |
| copyright | Springer-Verlag New York Inc. 1981 |
发表于 2025-3-21 18:54:45
