Complex Analytic Geometry

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538 Gerd Fischer

Complex AnalyticGeometry

Springer-Verlag Berlin. Heidelberg. New York 1976

Author Gerd Fischer Mathematisches Institut der Universit~t Mi]nchen TheresienstraBe 39 8 0 0 0 MLinchen 2 / B R D

Library of Congress Cataloging in Publication D a t a

Fischer, Gerd, 1939Complex analytic geometry. (Lecture notes in mathematics ; 538) 1. Functions of several complex variables. 2. Analytic spaces. 3~ Fiber spaces (Mathematics) I. Title. II. Series: Lecture notes in mathematics (Berlin) ; 538.

QA3.L28

vol. 538

[CA331]

~lO'.8s

[515'.94]

76-27692

AMS Subject Classifications (1970): 32 BXX, 32CXX, 32J10, 32LXX ISBN 3-540-07857-6 ISBN 0-387-07857-6

Springer-Verlag Berlin 9 Heidelberg 9 New York Springer-Verlag New York 9 Heidelberg 9 Berlin

This .w.ork is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under w 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. 9 by Springer-Verlag Berlin 9 Heidelberg 1976 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr.

PREFACE

These Lecture

Notes arose

of Regensburg, to present

Frankfurt

from courses

and Munich.

held at the Universities

The aim of the courses was

a survey of the fundamental

"complex

analytic

geometry"

research

in this field.

(i.e.

concepts

and results of

the theory of functions

several complex variables)

and to approach

The choice of the material

was governed by the idea that the

presentation

should center on (not necessarily

spaces and their holomorphic

maps.

Progressing

mentals of this theory to problems particularly patience,

the current

of

long and arduous

task.

of current Bearing

state of

reduced.) complex from the funda-

interest

is a

in mind the reader's

the length of the notes and last but not least the

energy of the author,

several basic but voluminous

methods

are easily accessible

in the literature

[3],

proofs have only been cited or sketched, [40],

[44],

[50],

[51],

[55],

[56],

particularly

(e.g.

[57],

[]],

[72],

[107],

[150]). Among these topics are the theory of sheaves,

of local analytic holomorphic

algebras

functions

and their dimensions,

in ~n including

the elementary

and finally the fundamental

Although

these notes are far from being self-contained,

as well as Theorems

tention was to provide

presentation

within

"elements

the framework

My sincere suggested

of analytic

Maurer

geometry"

improvements

Aman for proof-reading

Hopefully

is long overdue. the lectures

manuscript,

and to Joseph Maurer

of the

for their

to many colleagues

to Inge Pfeilschifter

the camera-ready

of

the in-

for a compendium

and their endurance,

comments,

for preparing

figures.

which

th