Local Analytic Geometry Basic Theory and Applications
Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of alge
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Local Analytic Geometry
Advanced Lectures in Mathematics
Editorial board:
Prof. Dr. Martin Aigner, Freie UniversWit Berlin, Germany Prof. Dr. Gerd Fischer, Heinrich-Heine-Universitat Diisseldorf, Germany Prof. Dr. Michael Griiter, Universitat des Saarlandes, Saarbriicken, Germany Prof. Dr. Rudolf Scharlau, Universitat Dortmund, Germany Prof. Dr. Gisbert Wiistholz, ETH Ziirich, Switzerland
Introduction to Markov Chains
Ehrhard Behrends
Einfiihrung in die Symplektische Geometrie
Rolf Berndt
Wavelets - Eine Einfiihrung
Christian Blatter
Local Analytic Geometry
Theo de Jong, Gerhard Pfister Dirac-Operatoren in der Riemannschen Geometrie
Thomas Friedrich
Hypergeometric Summation
Wolfram Koepf
The Steiner Tree Problem
Hans-Jiirgen Promel, Angelika Steger
The Basic Theory of Power Series
Jesus M. Ruiz
vieweg __________________
Theo de Jong Gerhard Pfister
Local Analytic Geometry Basic Theory and Applications
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Dr. Theo de Tong UniversWit des Saarlandes Fachbereich Mathematik Postfach 15 11 50 D-66041 Saarbriicken, Germany [email protected] Prof. Dr. Gerhard Pfister Universitat Kaiserslautern Fachbereich Mathematik Erwin-Schrtidinger-Str. 0-67663 Kaiserslautern, Germany [email protected]
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All rights reserved © Springer Fachmedien Wiesbaden , 2000 Originally published by Friedr. Vieweg & Sohn Verlagsgesellschaft mbH,BraunschweigIWiesbaden in 2000. Vieweg is a company in the specialist publishing group BertelsmannSpringer.
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ISBN 978-3-528-03137-4
ISBN 978-3-322-90159-0 (eBook)
DOI 10.1007/978-3-322-90159-0
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Voor Jeannette, Nils en Noah Fur Marlis
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Preface Algebraic geometry is, loosely speaking, concerned with the study of zero sets of polynomials (over an algebraically closed field). As one often reads in prefaces of introductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult to understand without the geometric motivation from which it has often developed. Local analytic geometry is concerned with germs of zero sets of analytic functions, that is, the study of such sets in the neighborhood of a point. It is not too big a surprise that the basic theory of local analytic geometry is, in many respects, similar to the basic theory of algebraic geometry. It would, therefore, appear to be a sensible idea to develop the two theories simultaneously. This, in fact, is not what we will do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult
