Introduction to singularities and deformations /
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| Author / Creator: | Greuel, G.-M. (Gert-Martin) |
|---|---|
| Imprint: | Berlin : Springer, 2007. |
| Description: | xii, 471 p. : ill. ; 25 cm. |
| Language: | English |
| Series: | Springer monographs in mathematics, 1439-7382 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/6277409 |
Table of Contents:
- Chapter I. Singularity Theory
- 1. Basic Properties of Complex Spaces and Germs
- 1.1. Weierstraß Preparation and Finiteness Theorem
- 1.2. Application to Analytic Algebras
- 1.3. Complex Spaces
- 1.4. Complex Space Germs and Singularities
- 1.5. Finite Morphisms and Finite Coherence Theorem
- 1.6. Applications of the Finite Coherence Theorem
- 1.7. Finite Morphisms and Flatness
- 1.8. Flat Morphisms and Fibres
- 1.9. Normalization and Non-Normal Locus
- 1.10. Singular Locus and Differential Forms
- 2. Hypersurface Singularities
- 2.1. Invariants of Hypersurface Singularities
- 2.2. Finite Determinacy
- 2.3. Algebraic Group Actions
- 2.4. Classification of Simple Singularities
- 3. Plane Curve Singularities
- 3.1. Parametrization
- 3.2. Intersection Multiplicity
- 3.3. Resolution of Plane Curve Singularities
- 3.4. Classical Topological and Analytic Invariants
- Chapter II. Local Deformation Theory
- 1. Deformations ofComplexSpace Germs
- 1.1. Deformations ofSingularities
- 1.2. Embedded Deformations
- 1.3. Versal Deformations
- 1.4. Infinitesimal Deformations
- 1.5. Obstructions
- 2. Equisingular Deformations of Plane Curve Singularities
- 2.1. Equisingular Deformations of the Equation
- 2.2. The Equisingularity Ideal
- 2.3. Deformations of the Parametrization
- 2.4. Computation of T 1 and T 2
- 2.5. Equisingular Deformations of the Parametrization
- 2.6. Equinormalizable Deformations
- 2.7. ¿-Constant and ¿-Constant Stratum
- 2.8. Comparison of Equisingular Deformations
- Appendix A. Sheaves
- A.1. Presheaves and Sheaves
- A.2. Gluing Sheaves
- A.3. Sheaves ofRings and Modules
- A.4. Image and Preimage Sheaf
- A.5. Algebraic Operations on Sheaves
- A.6. Ringed Spaces
- A.7. Coherent Sheaves
- A.8. Sheaf Cohomology
- A.9. Čech Cohomology and Comparison
- Appendix B. Commutative Algebra
- B.1. Associated Primes and Primary Decomposition
- B.2. Dimension Theory
- B.3. Tensor Product and Flatness
- B.4. Artin-Rees and Krull Intersection Theorem
- B.5. The Local Criterion of Flatness
- B.6. The Koszul Complex
- B.7. Regular Sequences and Depth
- B.8. Cohen-Macaulay, Flatness and Fibres
- B.9. Auslander-Buchsbaum Formula
- Appendix C. Formal Deformation Theory
- C.1. Functors of Artin Rings
- C.2. Obstructions
- C.3. The Cotangent Complex
- C.4. Cotangent Cohomology
- C.5. Relation to Deformation Theory
- References
- Index
