Lectures on Riemann Surfaces

Descripción

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 268 pp. Englisch.

N° de ref. del artículo 9780387906171

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Detalles bibliográficos

Título

Lectures on Riemann Surfaces

Editor

Springer New York, Springer New York Nov 1981

Fecha de publicación

1981

Idioma

Inglés

ISBN 10

0387906177

ISBN 13

9780387906171

Encuadernación

Buch

Edición

4ª Edición

Estado

Neu

Dimensiones

241 mm an. × 160 al. × 21 l. 241 milímetros de ancho por 160 de alto por 21 de largo

Peso

571 gramos

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