The valuative tree

Charles Favre, Mattias Jonsson (auth.)3540229841, 9783540229841

This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.

Table of contents :
Front Matter….Pages I-XV
Introduction….Pages 1-7
1. Generalities….Pages 9-24
2. MacLane’s Method….Pages 25-42
3. Tree Structures….Pages 43-80
4. Valuations Through Puiseux Series….Pages 81-96
5. Topologies….Pages 97-110
6. The Universal Dual Graph….Pages 111-150
7. Tree Measures….Pages 151-192
8. Applications of the Tree Analysis….Pages 193-209
Appendix….Pages 211-225
References….Pages 227-229
Index….Pages 231-234
Errata….Pages 241-241
Errata….Pages 241-243
Errata….Pages 243-243
Errata….Pages 243-243
Errata….Pages 243-244