From Holomorphic Functions to Complex Manifolds (Hardcover)

Klaus Fritzsche

ISBN 10: 0387953957 / ISBN 13: 9780387953953

Edité par Springer-Verlag New York Inc., New York, NY, 2002

Hardcover. The aim of this book is to give an understandable introduction to the the ory of complex manifolds. With very few exceptions we give complete proofs. Many examples and figures along with quite a few exercises are included. Our intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involved with sheaves, coherence, and higher-dimensional cohomology are avoided. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional co cycles are used. Nevertheless, deep results can be proved, for example the Remmert-Stein theorem for analytic sets, finiteness theorems for spaces of cross sections in holomorphic vector bundles, and the solution of the Levi problem. The first chapter deals with holomorphic functions defined in open sub sets of the space en. Many of the well-known properties of holomorphic functions of one variable, such as the Cauchy integral formula or the maxi mum principle, can be applied directly to obtain corresponding properties of holomorphic functions of several variables. Furthermore, certain properties of differentiable functions of several variables, such as the implicit and inverse function theorems, extend easily to holomorphic functions. This book is an introduction to the theory of complex manifolds. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9780387953953

Synopsis :

This book is an introduction to the theory of complex manifolds. The authors's intent is to familiarize the reader with the most important branches and methods in complex analysis of several variables and to do this as simply as possible. Therefore, the abstract concepts involving sheaves, coherence, and higher-dimensional cohomology have been completely avoided. Each chapter is complemented by a variety of examples and exercises. The only prerequisite needed to read this book is a knowledge of real analysis and some basic facts from algebra, topology, and the theory of one complex variable.

Détails bibliographiques

Titre : From Holomorphic Functions to Complex ...
Éditeur : Springer-Verlag New York Inc., New York, NY
Date d'édition : 2002
Reliure : Hardcover
Etat : new
Edition : Edition originale