Topics on Real and Complex Singularities: An Introduction by Alexandru Dimca (Ge

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Topics on Real and Complex Singularities by Alexandru Dimca

The body of mathematics developed in the last forty years or so which can be put under the heading Singularity Theory is quite large. And the excellent introductions to this vast sub­ ject which are already available (for instance [AGVJ, [BGJ, [GiJ, [GGJ, [LmJ, [Mr], [WsJ or the more advanced [Ln]) cover necessarily only apart of even the most basic topics. The aim of the present book is to introduce the reader to a few important topics from ZoaaZ Singularity Theory. Some of these topics have already been treated in other introductory books (e.g. right and contact finite determinacy of function germs) while others have been considered only in papers (e.g. Mather's Lemma, classification of simple O-dimensional complete intersection singularities, singularities of hyperplane sections and of dual mappings of projective hypersurfaces). Even in the first case, we feel that our treatment is different from the introductions mentioned above - the general reason being that we give special attention to the aompZex anaZytia situation and to the connections with AZgebraia Geometry. We offer now a detailed description of the contents, pOint­ ing out special aspects and new material (i.e. previously un­ published, though for the most part surely known to the~ts!). Chapter 1 is a short introduction for the beginner. We recall here two basic results (the Submersion Theorem and Morse Lemma) and make a few comments on what is meant by the local behaviour of a function or of a plane algebraic cur

FORMAT
Paperback LANGUAGE
German CONDITION
Brand New Publisher Description

The body of mathematics developed in the last forty years or so which can be put under the heading Singularity Theory is quite large. And the excellent introductions to this vast sub- ject which are already available (for instance [AGVJ, [BGJ, [GiJ, [GGJ, [LmJ, [Mr], [WsJ or the more advanced [Ln]) cover necessarily only apart of even the most basic topics. The aim of the present book is to introduce the reader to a few important topics from ZoaaZ Singularity Theory. Some of these topics have already been treated in other introductory books (e.g. right and contact finite determinacy of function germs) while others have been considered only in papers (e.g. Mather's Lemma, classification of simple O-dimensional complete intersection singularities, singularities of hyperplane sections and of dual mappings of projective hypersurfaces). Even in the first case, we feel that our treatment is different from the introductions mentioned above - the general reason being that we give special attention to the aompZex anaZytia situation and to the connections with AZgebraia Geometry. We offer now a detailed description of the contents, pOint- ing out special aspects and new material (i.e. previously un- published, though for the most part surely known to the ts!). Chapter 1 is a short introduction for the beginner. We recall here two basic results (the Submersion Theorem and Morse Lemma) and make a few comments on what is meant by the local behaviour of a function or of a plane algebraic curve.

Table of Contents

1: Two Classical Examples: Submersion Theorem and Morse Lemma.- 2: Germs and Jets.- 3: Equivalence Relations on Germs and Jets.- 4: Tangent Spaces to Orbits.- 5: Basic Classification Examples in Linear Algebra and Algebraic Geometry.- 6: Finite Determinacy of Map Germs.- 7: Weighted Homogeneous Singularities.- 8: Classification of Simple Singularities of Functions.- 9: Classification of Simple O-Dimensional Complete Intersections.- 10: Curve and Surface Singularities.- 11: Dual Mappings and Contact Tangency Classes for Projective Hypersurfaces.- Appendix: Two Recent Research Topics.- References.- List of Notations.

Long Description

The body of mathematics developed in the last forty years or so which can be put under the heading Singularity Theory is quite large. And the excellent introductions to this vast sub

Details ISBN3528089997 Year 1987 ISBN-10 3528089997 ISBN-13 9783528089993 Format Paperback Edition Description 1987 Series Advanced Lectures in Mathematics Media Book DEWEY 510 Imprint Friedrich Vieweg & Sohn Verlagsgesellschaft mbH Place of Publication Wiesbaden Country of Publication Germany Short Title GER-TOPICS ON REAL & COMPLEX S Language German Author Alexandru Dimca Edition 1987th Subtitle An Introduction DOI 10.1007/978-3-663-13903-4 Pages 242 Publisher Friedrich Vieweg & Sohn Verlagsgesellschaft mbH Publication Date 1987-01-01 Illustrations XVII, 242 S. Audience Undergraduate Country of Origin US Product Class Description Mathematics Alternative 9783663139034
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