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。《完全交上的孤立奇点(第2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。
《完全交上的孤立奇点(第2版)》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。《完全交上的孤立奇点(第2版)》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。《完全交上的孤立奇点(第2版)》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。
E.J.N.LOOIJENGA，荷兰乌得勒支大学教授，荷兰皇家艺术与科学院院士。曾在1978年的国际数学家大会和1992年的欧洲数学家大会做邀请报告。
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 (localcase)
3.B Monodromy of a quadratic singularity (globalcase)
Chapter 4 Critical Space and Discriminant Space
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 (localcase)
3.B Monodromy of a quadratic singularity (globalcase)
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 versaldeformations
Chapter 7 Vanishing Lattices, Monodromy Groups andAdjacency
7.A The fundamental group of a hypersurfacecomplement
7.B The monodromy group
7.C Adjacency
7.D A partial classification
Chapter 8 The Local Gauβ-Manin Connection
8.A De Rham cohomology of good representatives
8.B The Gauβ-Manin connection
8.C The complete intersection case
Chapter 9 Applications of the Local Gauβ-ManinConnection
9.A Milnor number and Tjurina number
9.B Singularities with good Cx-action
9.C A period mapping
Bibliography
Index of Notations
Subject Index
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