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Book Cover
E-book
Author Greuel, G.-M. (Gert-Martin)

Title Introduction to singularities and deformations / G.-M. Greuel, C. Lossen, E. Shustin
Published Berlin : Springer, 2007

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Description 1 online resource (xii, 471 pages) : illustrations
Series Springer monographs in mathematics, 1439-7382
Springer monographs in mathematics. 1439-7382
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
Summary "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 in 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."--Jacket
Bibliography Includes bibliographical references (pages 447-453) and index
Notes Print version record
In Springer e-books
Subject Singularities (Mathematics)
Deformations of singularities.
MATHEMATICS -- Complex Analysis.
Deformations of singularities.
Singularities (Mathematics)
Deformations of singularities.
Singularities (Mathematics)
Form Electronic book
Author Lossen, Christoph.
Shustin, Eugenii.
ISBN 9783540284192
3540284192
3540283803
9783540283805
6610803730
9786610803736