Valuations and multiplier ideals

Favre, Charles; Jonsson, Mattias

doi:10.1090/S0894-0347-05-00481-9

Valuations and multiplier ideals
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by Charles Favre and Mattias Jonsson

J. Amer. Math. Soc. 18 (2005), 655-684

DOI: https://doi.org/10.1090/S0894-0347-05-00481-9

Published electronically: 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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