The Valuative Tree
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.
- PDF / 3,873,906 Bytes
- 251 Pages / 439 x 666 pts Page_size
- 69 Downloads / 172 Views
1853
Charles Favre Mattias Jonsson
The Valuative Tree
123
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 thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science + Business Media http://www.springeronline.com c Springer-Verlag Berlin Heidelberg 2004 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the authors 41/3142/du - 543210 - Printed on acid-free paper
To Muriel and Johanna
Preface
This book grew out of a common passion for a beautiful natural object that we decided to call the “valuative tree”. Motivated by questions stemming from complex dynamics and complex analysis, we realized that we needed to understand the link between valuations, which are purely algebraic objects, and more geometric or analytic constructions such as blowups or Lelong numbers. More precisely, we looked at the structure of a special set of valuations, and we found that this space had a very rich and delicate topological structure. We hope that the reader will share our enthusiasm while progressively exploring this space into its finer details all along this book. This monograph has benefited from the help of many people. The first author wishes to warmly thank Bernard Teissier for his constant support and help, and Patrick Popescu-Pampu, Mark Spivakovsky and Michel Vaqui´e for fruitful discussions. The second author expresses his gratitude to JeanFran¸cois Lafont, Robert Lazarsfeld and Karen Smith. We both thank the referees for a number of useful suggestions. Our work was done at several places, including the Institut de Math´ematiques in Paris, the Department of Mathematics of the University of Michigan in Ann Arbor, RIMS in Kyoto and IMPA in Rio de Janeiro. We are grateful to these institutions for having provided
Data Loading...
