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.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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Charles Favre Mattias Jonsson
The Valuative Tree
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Authors Charles Favre CNRS Institut de Math´ematique de Jussieu Universit´e Denis Diderot Case 7012 2, place Jussieu 75251 Paris Cedex 05 France e-mail:
[email protected] Mattias Jonsson Department of Mathematics University of Michigan Ann Arbor, MI 48109-1109 U.S.A. e-mail:
[email protected]
Cover picture: Arriving Ambrosden by Heather Power
Library of Congress Control Number: 2004110772
Mathematics Subject Classification (2000): 14H20, 13A18, 54F50 ISSN 0075-8434 ISBN 3-540-22984-1 Springer Berlin Heidelberg New York DOI: 10.1007/b100262 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts