Valuations and multiplier ideals

Details Valuations and multiplier ideals Valuations and multiplier ideals

2004-06-07

arxiv.org/abs/math/0406109v2

Mathematics

Complex Variables

32 pages, 3 figures. To appear in J. Amer. Math. Soc

Scientific paper

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 Kollar. 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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