奇異性理論將代數(shù)幾何、解析幾何和微分分析聯(lián)系在一起。比較易處理或者較自然的奇點(diǎn)為孤立完全交奇點(diǎn)。在過(guò)去幾十年里。在理解奇點(diǎn)理論以及它們的變形方面有了很多研究與進(jìn)展。
《完全交上的孤立奇點(diǎn)》的第一版是作者路易安嘎在耶魯大學(xué)關(guān)于奇點(diǎn)課程以及在荷蘭萊頓、奈梅亨和烏得勒支三地兩年的討論班講義的基礎(chǔ)上寫成的。《完全交上的孤立奇點(diǎn)(第2版)》簡(jiǎn)化了某些證明，加強(qiáng)了某些結(jié)論，對(duì)一些材料進(jìn)行重整，并補(bǔ)充了小部分內(nèi)容。
《完全交上的孤立奇點(diǎn)(第2版)》的目的是提供給讀者復(fù)空間奇點(diǎn)尤其是完全交上的奇點(diǎn)的介紹。《完全交上的孤立奇點(diǎn)(第2版)》所需的預(yù)備知識(shí)為代數(shù)幾何、解析幾何、代數(shù)拓?fù)湟恍┲R(shí)、另外還需了解Stein空間的一些結(jié)論�！锻耆簧系墓铝⑵纥c(diǎn)(第2版)》可供代數(shù)幾何、復(fù)解析幾何和微分分析方面的研究生和相關(guān)研究人員參考。
E.J.N.LOOIJENGA，荷蘭烏得勒支大學(xué)教授，荷蘭皇家藝術(shù)與科學(xué)院院士。曾在1978年的國(guó)際數(shù)學(xué)家大會(huì)和1992年的歐洲數(shù)學(xué)家大會(huì)做邀請(qǐng)報(bào)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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