| Description |
1 online resource (xi, 200 pages) : illustrations |
| Series |
London Mathematical Society lecture note series ; 77 |
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London Mathematical Society lecture note series ; 77.
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| Contents |
Cover; Title; Copyright; Dedication; Contents; INTRODUCTION; CHAPTER 1 : EXAMPLES OF ISOLATED SINGULAR POINTS; A. Hypersurface singularities; B. Complete intersections; C. Quotient singularities; D. Quasi-conical singularities; E. Cusp singularities; CHAPTER 2: THE MILNOR FI BRAT I ON; A. The link of an isolated singularity; B. Good representatives; C. Geometric monodromy; D. Excellent representatives; CHAPTER 3: PICARD-LEFSCHETZ FORMULAS; A. Monodromy of a quadratic singularity (local case); B. Monodromy of a quadratic singularity (global case) |
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CHAPTER 4: CRITICAL SPACE AND DISCRIMINANT SPACEA. The critical space; B. The Thorn singularity manifolds; C. Development of the discriminant locus; D. Fitting ideals; E. The discriminant space; CHAPTER 5: RELATIVE MONODROMY; A. The basic construction; B. The homotopy type of the Mil nor fibre; C. The monodromy theorem; CHAPTER 6: DEFORMATIONS; A. Relative differentials; B. The Kodaira-Spencer map; C. Versal deformations; D. Some analytic properties of versal deformations; CHAPTER 7: VANISHING LATTICES, M0N0DR0MY GROUPS AND ADJACENCY; A. The fundamental group of a hypersurface complement |
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B. The monodromy goupC. Adjacency; D.A partial classification; CHAPTER 8: THE LOCAL GAUSS-MAN IN CONNECTION; A. De Rham cohomology of good representatives; B. The Gauss-Manin connection; C. The complete intersection case; CHAPTER 9: APPLICATIONS OF THE LOCAL GAUSS-MANIN CONNECTION; A. Milnor number and Tjurina number; B. Singularities with good C*-action; C.A period mapping; REFERENCES; INDEX OF NOTATIONS; SUBJECT INDEX |
| Summary |
Singularity theory is not a field in itself, but rather an application of algebraic geometry, analytic geometry and differential analysis. The adjective 'singular' in the title refers here to singular points of complex-analytic or algebraic varieties or mappings. A tractable (and very natural) class of singularities to study are the isolated complete intersection singularities, and much progress has been made over the past decade in understanding these and their deformations |
| Bibliography |
Includes bibliographical references (pages 187-195) |
| Notes |
Includes indexes |
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Print version record |
| Subject |
Geometry, Algebraic.
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Singularities (Mathematics)
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MATHEMATICS -- Geometry -- Algebraic.
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Geometry, Algebraic
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Singularities (Mathematics)
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Isolierte Singularität
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Vollständiger Durchschnitt
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Algebraische Geometrie
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Géométrie algébrique.
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Singularités (mathématiques)
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| Form |
Electronic book
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| ISBN |
9781107361188 |
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1107361184 |
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9780511662720 |
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0511662726 |
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