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
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