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Journal of the American Mathematical Society

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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
Published electronically: April 13, 2005
MathSciNet review: 2138140
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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

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

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.