奇异性理论将代数几何、解析几何和微分分析联系在一起。比较易处理或者较自然的奇点为孤立完全交奇点。在过去几十年里。在理解奇点理论以及它们的变形方面有了很多研究与进展。
《完全交上的孤立奇点》的第一版是作者路易安嘎在耶鲁大学关于奇点课程以及在荷兰莱顿、奈梅亨和乌得勒支三地两年的讨论班讲义的基础上写成的。第二版简化了某些证明，加强了某些结论，对一些材料进行重整，并补充了小部分内容。
本书的目的是提供给读者复空间奇点尤其是完全交上的奇点的介绍，所需的预备知识为代数几何、解析几何、代数拓扑一些知识、另外还需了解Stein空间的一些结论。本书可供代数几何、复解析几何和微分分析方面的研究生和相关研究人员参考。
- Front Matter
- Chapter 1 Examples of Isolated Singular Points
- 1.A Hypersurface singularities
- 1.B Complete intersections
- 1.C Quotient singularities
- 1.D Quasi-conical singularities
- 1.E Cusp singularities
- Chapter 2 The Milnor Fibration
- 2.A The link of an isolated singularity
- 2.B Good representatives
- 2.C Geometric monodromy
- 2.D*Excellent representatives
- Chapter 3 Picard-Lefschetz Formulae
- 3.A Monodromy of a quadratic singularity (local case)
- 3.B Monodromy of a quadratic singularity (global case)
- Chapter 4 Critical Space and Discriminant Space
- 4.A The critical space
- 4.B The Thom singularity manifolds
- 4.C Development of the discriminant locus
- 4.D The discriminant space
- 4.E Appendix: Fitting ideals
- Chapter 5 Relative Monodromy
- 5.A The basic construction
- 5.B The homotopy type of the Milnor fiber
- 5.C The monodromy theorem
- Chapter 6 Deformations
- 6.A Relative differentials
- 6.B The Kodaira-Spencer map
- 6.C Versal deformations
- 6.D Some analytic properties of versal deformations
- Chapter 7 Vanishing Lattices, Monodromy Groups and Adjacency
- 7.A The fundamental group of a hypersurface complement
- 7.B The monodromy group
- 7.C Adjacency
- 7.D A partial classification
- Chapter 8 The Local Gauß-Manin Connection
- 8.A De Rham cohomology of good representatives
- 8.B The Gaus-Manin connection
- 8.C The complete intersection case
- Chapter 9 Applications of the Local Gauß-Manin Connection
- 9.A Milnor number and Tjurina number
- 9.B Singularities with good C×-action
- 9.C A period mapping
- Bibliography
- Index of Notations
- Subject Index
- 版权
