Author(s): Alexandru Dimca
Series: Advanced lectures in mathematics
Publisher: Friedrich Vieweg & Sohn Verlag
Year: 1987
Language: English
Pages: 258
Table of Contents......Page 5
Introduction......Page 8
1. Two Classical Examples: Submersion Theorem and Morse Lemma......Page 17
§1. Germs of sets and mappings......Page 21
§2. Basic properties of the algebras E_n......Page 23
§3. Jets of mappings......Page 28
§1. Group actionsand equivalence relations......Page 30
§2. Germs of complex analytic spaces......Page 35
§3. Group actions on jet spaces......Page 43
§1. Semialgebraic sets......Page 46
§2. Tangent spaces and transversals......Page 50
§3. Tangent spaces to orbits in jet spaces......Page 53
§4. Mather's Lemma......Page 56
§1. Linear maps and quadratic forms......Page 59
§2. Cubic forms and plane cubic curves......Page 63
§3. Pencils of quadrics......Page 71
§4. Pencils of binary cubic forms......Page 73
§1. R-finite determinacy......Page 78
§2. K-finite determinacy and isolated singularities of complete intersections......Page 90
§3. Generic properties of map germs......Page 100
§4. Milnor number and Tjurina number......Page 106
§1. Weighted homogeneous polynomials and C^*-actions......Page 115
§2. Finitely determined weighted homogeneous singularities......Page 121
§3. Semi weighted homogeneous singularities......Page 131
§4. Around a theorem of K. Saito......Page 135
§5. Uniqueness of weighted homogeneity type......Page 140
§1. Simple singularities and adjacency......Page 144
§2. Complete transversals and Splitting Lemma......Page 149
§3. Classification of K-simple function singularities......Page 152
§4. Classification of R-simple function singularities......Page 160
§1. Further invariants for singularities: Boardman symbol and Hilbert-Samuel function......Page 163
§2. Normal forms and specializations......Page 168
§1. Weierstrass normal form and blowing-up......Page 184
§2. Invariants of plane curve singularities......Page 188
§3. Blowing-up plane curve singularities......Page 195
§4. Basic facts on resolution of surface singularities......Page 203
§5. Some properties of simple surface singularities......Page 208
§1. The dual mapping and the dual variety......Page 220
§2. Contact tangency classes......Page 231
§3. Hyperplane sections of generic hypersurfaces......Page 236
Appendix: Two Recent Research Topics......Page 246
References......Page 248
List of Notations......Page 252
Index......Page 254
