Journal of the American Mathematical Society

Author(s): Charles Favre; Mattias Jonsson
Journal: J. Amer. Math. Soc. 18 (2005), 655-684.
MSC (2000): Primary 14B05; Secondary 32U25, 13H05
Posted: April 13, 2005
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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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Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14B05, 32U25, 13H05

Charles Favre
Affiliation: CNRS, Institut de Mathématiques, Equipe Géométrie et Dynamique, F-75251 Paris Cedex 05, France
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
Email: mattiasj@umich.edu, mattiasj@kth.se

DOI: 10.1090/S0894-0347-05-00481-9
PII: S 0894-0347(05)00481-9
Keywords: Valuations, multiplier ideals, singularity exponents, Arnold multiplicity, Lelong numbers, Kiselman numbers, trees, Laplace operator.
Received by editor(s): January 16, 2004
Posted: April 13, 2005
Additional Notes: The second author was partially supported by NSF Grant No. DMS-0200614
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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ISSN: 1088-6834(e) ISSN: 0894-0347(p)

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