Introduction to Singularities and Deformations by Gert-Martin Greuel (English) H

The Nile on eBay   Introduction to Singularities and Deformations by Gert-Martin Greuel, Christoph Lossen, Eugenii I. Shustin

Presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. This introductory text provides the general framework of the theory. It develops the relevant techniques, including the Weierstrass preparation theorem and the finite coherence theorem.

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete. In the first part of the book the authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained.The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thuscan serve as source for special courses in singularity theory and local algebraic and analytic geometry.

Back Cover

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete. In the first part of the book the authors develop the relevant techniques, including the Weierstra

Table of Contents

I. Singularity Theory. Basic Properties of Complex Spaces and Germs. Weierstrass Preparation and Finiteness Theorem. Application to Analytic Algebras. Complex Spaces. Complex Space Germs and Singularities. Finite Morphisms and Finite Coherence Theorem. Applications of the Finite Coherence Theorem. Finite Morphisms and Flatness. Flat Morphisms and Fibres. Singular Locus and Differential Forms. Hypersurface Singularities. Invariants of Hypersurface Singularities. Finite Determinacy. Algebraic Group Actions. Classification of Simple Singularities. Plane Curve Singularities. Parametrization. Intersection Multiplicity. Resolution of Plane Curve Singularities. Classical Topological and Analytic Invariants.- II. Local Deformation Theory. Deformations of Complex Space Germs. Deformations of Singularities. Embedded Deformations. Versal Deformations. Infinitesimal Deformations. Obstructions. Equisingular Deformations of Plane Curve Singularities.- Equisingular Deformations of the Equation. The Equisingularity Ideal. Deformations of the Parametrization. Computation of T^1 and T^2 . Equisingular Deformations of the Parametrization. Equinormalizable Deformations. Versal Equisingular Deformations.- Appendices: Sheaves. Commutative Algebra. Formal Deformation Theory. Literature.- Index.

Review

From the reviews:"This monograph is dedicated to the theory of singularities, a subject with a central role in modern mathematics. … This very well written book has a unified point of view based on the theory of analytic spaces, which allows a coherent presentation of both of its main themes: the theory of singularities and deformations of singularities. … The book includes many examples and exercises … . This monograph can serve as a source for several special courses in singularity theory and local analytic geometry." (Vasile Brînzanescu, Mathematical Reviews, Issue 2008 b)

Long Description

Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete. In the first part of the book the authors develop the relevant techniques, including the Weierstra preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formaldeformation theory, make the reading self-contained.The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.

Review Quote

From the reviews: "This monograph is dedicated to the theory of singularities, a subject with a central role in modern mathematics. ... This very well written book has a unified point of view based on the theory of analytic spaces, which allows a coherent presentation of both of its main themes: the theory of singularities and deformations of singularities. ... The book includes many examples and exercises ... . This monograph can serve as a source for several special courses in singularity theory and local analytic geometry." (Vasile Brnzanescu, Mathematical Reviews, Issue 2008 b)

Feature

The material is for the first time exposed from a unified point of view Material is supplied with complete proofs (new in many cases), and can serve as source for special courses in singularity theory. Three appendices, including basic facts from the sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained

Description for Sales People

This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. The authors develop the relevant techniques, including Weierstra

Details ISBN3540283803 Short Title INTRO TO SINGULARITIES & DEFOR Series Springer Monographs in Mathematics Language English ISBN-10 3540283803 ISBN-13 9783540283805 Media Book Format Hardcover Year 2006 Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K Place of Publication Berlin Country of Publication Germany DEWEY 516.35 Birth 1961 DOI 10.1007/b79898;10.1007/3-540-28419-2 Author Eugenii I. Shustin Pages 472 Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Edition Description 2007 ed. Edition 2007th Publication Date 2006-11-29 Alternative 9783642066580 Illustrations 54 Illustrations, black and white; XII, 472 p. 54 illus. Audience Undergraduate We've got this

At The Nile, if you're looking for it, we've got it.With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love!

TheNile_Item_ID:96224161;