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The Valuative Tree

  • Book
  • © 2004

Overview

Authors:
  1. Charles Favre
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  2. Mattias Jonsson
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1853)

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Table of contents (17 chapters)

  1. Front Matter

    Pages I-XV
    Download chapter PDF

  2. Introduction

    • Charles Favre, Mattias Jonsson
    Pages 1-7

  3. 1. Generalities

    • Charles Favre, Mattias Jonsson
    Pages 9-24

  4. 2. MacLane’s Method

    • Charles Favre, Mattias Jonsson
    Pages 25-42

  5. 3. Tree Structures

    • Charles Favre, Mattias Jonsson
    Pages 43-80

  6. 4. Valuations Through Puiseux Series

    • Charles Favre, Mattias Jonsson
    Pages 81-96

  7. 5. Topologies

    • Charles Favre, Mattias Jonsson
    Pages 97-110

  8. 6. The Universal Dual Graph

    • Charles Favre, Mattias Jonsson
    Pages 111-150

  9. 7. Tree Measures

    • Charles Favre, Mattias Jonsson
    Pages 151-192

  10. 8. Applications of the Tree Analysis

    • Charles Favre, Mattias Jonsson
    Pages 193-209

  11. Appendix

    • Charles Favre, Mattias Jonsson
    Pages 211-225

  12. References

    • Charles Favre, Mattias Jonsson
    Pages 227-229

  13. Index

    • Charles Favre, Mattias Jonsson
    Pages 231-234

  14. Errata

    • Charles Favre, Mattias Jonsson
    Pages 241-241

  15. Errata

    • Charles Favre, Mattias Jonsson
    Pages 241-243

  16. Errata

    • Charles Favre, Mattias Jonsson
    Pages 243-243

  17. Errata

    • Charles Favre, Mattias Jonsson
    Pages 243-243

  18. Errata

    • Charles Favre, Mattias Jonsson
    Pages 243-244
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About this book

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.

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