Valuations and multiplier ideals
Authors:
Charles Favre and Mattias Jonsson
Journal:
J. Amer. Math. Soc. 18 (2005), 655-684
MSC (2000):
Primary 14B05; Secondary 32U25, 13H05
DOI:
https://doi.org/10.1090/S0894-0347-05-00481-9
Published electronically:
April 13, 2005
MathSciNet review:
2138140
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We present a new approach to the study of multiplier ideals in a local, two-dimensional setting. Our method allows us to deal with ideals, graded systems of ideals and plurisubharmonic functions in a unified way. Among the applications are a formula for the complex integrability exponent of a plurisubharmonic function in terms of Kiselman numbers, and a proof of the openness conjecture by Demailly and Kollár. Our technique also yields new proofs of two recent results: one on the structure of the set of complex singularity exponents for holomorphic functions; the other by Lipman and Watanabe on the realization of ideals as multiplier ideals.
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Additional Information
Charles Favre
Affiliation:
CNRS, Institut de Mathématiques, Equipe Géométrie et Dynamique, F-75251 Paris Cedex 05, France
MR Author ID:
641179
Email:
favre@math.jussieu.fr
Mattias Jonsson
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Address at time of publication:
Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
MR Author ID:
631360
Email:
mattiasj@umich.edu, mattiasj@kth.se
Keywords:
Valuations,
multiplier ideals,
singularity exponents,
Arnold multiplicity,
Lelong numbers,
Kiselman numbers,
trees,
Laplace operator.
Received by editor(s):
January 16, 2004
Published electronically:
April 13, 2005
Additional Notes:
The second author was partially supported by NSF Grant No. DMS-0200614
Article copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.