归一化体积函数极小值的唯一性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-05-17 DOI:10.4310/cjm.2021.v9.n1.a2

Chenyang Xu, Ziquan Zhuang

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引用次数: 30

摘要

我们证实了池莉的一个猜想，即klt奇异性的归一化体积函数的极小值在重新缩放之前是唯一的。这是通过定义估值的稳定性阈值来实现的，然后证明估值是极小值，当且仅当它是K-半稳定的，并且K-半稳定性估值在重新缩放之前是唯一的。作为应用，我们证明了klt奇点体积的有限度公式和klt奇点的局部基群的有效界。

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Uniqueness of the minimizer of the normalized volume function

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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.