Jumping numbers of multiplier ideals and Kiselman’s Lelong numbers. (Chinese. English summary) Zbl 07802327

He, Bojie

Chin. Ann. Math., Ser. A 44, No. 3, 285-302 (2023).

Summary: This article aims at giving a more precise explanation of the relation between cluster points of jumping numbers and Kiselman’s refined Lelong numbers for toric plurisubharmonic functions. There are three applications. The first is to recover a recent result on the classification of cluster points of jumping numbers of planar toric plurisubharmonic functions in terms of Kiselman’s refined Lelong numbers in the direction of \((1, 0)\) and \((0, 1)\). The second is to obtain a dimensional result on the poles of toric plurisubharmonic functions with cluster points. The third is to confirm an equivalent formulation of v-equivalence in the special case of toric plurisubharmonic function. In the end, the author constructs other interesting examples on cluster points of log canonical thresholds at different points.

MSC:

32U05	Plurisubharmonic functions and generalizations
14F18	Multiplier ideals

Keywords:

plurisubharmonic function; multiplier ideal; jumping number; Kiselman’s Lelong number

References:

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