Description 
1 online resource (xii, 471 pages) : illustrations 
Series 
Springer monographs in mathematics, 14397382 

Springer monographs in mathematics. 14397382

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 447453) and index 
Notes 
Print version record 
In 
Springer ebooks 
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 
