乘子理想的跳跃数及Kiselman方向Lelong数

Jumping Numbers of Multiplier Ideals and Kiselman's Lelong Numbers

本文旨在给出环面多次调和函数的乘子理想跳跃数聚点和Kiselman方向Lelong数的更精确的关系.这有如下三个应用:第一,它从(1,0)和(0,1)方向Lelong数的角度出发,复原了最近关于二维环面多次调和函数聚点分类的一个结果;第二,它给出了带跳跃数聚点的环面多次调和函数的极点集维数的有关结果;第三,它给出了在环面多次调和函数这一特殊情形时,关于v-等价关系的一个等价刻画.最后,作者构造了一类多次调和函数,使得它们在一点处的对数标准阈值为在附近点列的对数标准阈值的严格递增极限.

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,O)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.