Lectures on Riemann Surfaces

Forster, Otto

ISBN 10: 0387906177 / ISBN 13: 9780387906171

Edité par Springer, 1981

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Détails bibliographiques

• Titre: Lectures on Riemann Surfaces
• Éditeur: Springer
• Date de parution: 1981
• Langue: anglais
• ISBN à 10 chiffres: 0387906177
• ISBN à 13 chiffres: 9780387906171
• Reliure: Couverture rigide
• Édition: 4ème Édition
• État de l'article: As New

A propos de ce titre

Synopsis

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.

Présentation de l'éditeur

This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."--MATHEMATICAL REVIEWS