TY  - GEN
AU  - Greuel, Gert-Martin
AU  - Lossen, Christoph, 
AU  - Shustin, Eugenii,
TI  - Introduction to singularities and deformations
SN  - 9783642066580
U1  - 515.942 
PY  - 2011///
CY  - London
PB  - Springer
KW  - Singularities (Mathematics)
KW  - Deformations of singularities
KW  - Geometry, Algebraic
N1  - 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
ER  -