Introduction to singularities and deformations/ Gert-Martin Greuel, Christoph Lossen, Eugenii Shustin.
Publication details: London: Springer, 2011Description: 471 p.: ill.; 24 cmISBN: 9783642066580Subject(s): Singularities (Mathematics) | Deformations of singularities | Geometry, AlgebraicDDC classification: 515.942Item type | Current library | Call number | Status | Date due | Barcode | Item holds |
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General Books | Central Library, Sikkim University | 515.942 GRE/I (Browse shelf(Opens below)) | Available | 48407 |
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
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