Uniqueness of the minimizer of the normalized volume function
Uniqueness of the minimizer of the normalized volume function
复制标题
DOI：
10.4310/cjm.2021.v9.n1.a2
复制
发表时间：
2020-05
影响因子：
1.6
通讯作者：
Chenyang Xu-;Ziquan Zhuang
中科院分区：
文献类型：
--
作者：
Chenyang Xu-;Ziquan Zhuang
我们证实了一个猜想池李说，最小的归一化体积函数的klt奇点是唯一的重新缩放。这是通过定义估值的稳定性阈值来实现的，然后证明一个估值是极小值当且仅当它是K-半稳定的，并且K-半稳定估值在重新标度之前是唯一的。作为应用，我们证明了klt奇点体积的有限度公式和klt奇点局部基本群的有效界。
We confirm a conjecture of Chi Li which says that the minimizer of the normalized volume function for a klt singularity is unique up to rescaling. This is achieved by defining stability thresholds for valuations, and then showing that a valuation is a minimizer if and only if it is K-semistable, and that K-semistable valuation is unique up to rescaling. As applications, we prove a finite degree formula for volumes of klt singularities and an effective bound of the local fundamental group of a klt singularity.