The Valuative Tree

  • Authors
  • Charles Favre
  • Mattias Jonsson

Part of the Lecture Notes in Mathematics book series (LNM, volume 1853)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Charles Favre, Mattias Jonsson
    Pages 1-7
  3. Charles Favre, Mattias Jonsson
    Pages 9-24
  4. Charles Favre, Mattias Jonsson
    Pages 25-42
  5. Charles Favre, Mattias Jonsson
    Pages 43-80
  6. Charles Favre, Mattias Jonsson
    Pages 81-96
  7. Charles Favre, Mattias Jonsson
    Pages 97-110
  8. Charles Favre, Mattias Jonsson
    Pages 111-150
  9. Charles Favre, Mattias Jonsson
    Pages 151-192
  10. Charles Favre, Mattias Jonsson
    Pages 193-209
  11. Charles Favre, Mattias Jonsson
    Pages 211-225
  12. Charles Favre, Mattias Jonsson
    Pages 227-229
  13. Charles Favre, Mattias Jonsson
    Pages 231-234
  14. Charles Favre, Mattias Jonsson
    Pages 241-241
  15. Charles Favre, Mattias Jonsson
    Pages 241-243
  16. Charles Favre, Mattias Jonsson
    Pages 243-243
  17. Charles Favre, Mattias Jonsson
    Pages 243-243
  18. Charles Favre, Mattias Jonsson
    Pages 243-244

About this book

Introduction

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.

Keywords

Graph Laplace operator Riemann-Zariski surface Zariski topology classification dual graphs trees valuations

Bibliographic information

  • DOI https://doi.org/10.1007/b100262
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-22984-1
  • Online ISBN 978-3-540-44646-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 0075-8434
  • About this book