论文标题
归一化体积函数的最小化器的唯一性
Uniqueness of the minimizer of the normalized volume function
论文作者
论文摘要
我们确认了Chi Li的猜想，该猜想说，KLT奇异性的归一化体积函数的最小化是独一无二的。这是通过定义估值的稳定阈值来实现的，然后在且仅当它是可以ksemessiste的时，并且ksemessissistable的估值是独一无二的。作为应用，我们证明了KLT奇点体积的有限度公式，并且是KLT奇异性的局部基本群体的有效界限。
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.
