Kähler–Einstein metrics near an isolated log-canonical singularity

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-06-10 DOI:10.1515/crelle-2022-0095

V. Datar, X. Fu, Jian Song

引用次数: 8

Abstract

Abstract We construct Kähler–Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2. We also establish a stability result for Kähler–Einstein metrics near certain types of isolated log canonical singularity. As application, for complex dimension 2 log canonical singularity, we show that any complete Kähler–Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to model Kähler–Einstein metrics from hyperbolic geometry.

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Kähler-Einstein在孤立对数规范奇点附近的度量

摘要本文在孤立对数正则(非对数终端)奇点附近构造具有负标量曲率的Kähler-Einstein度量。如果底层空间具有复杂的维度2，那么这些度量在奇点附近是完整的。我们还建立了Kähler-Einstein指标在某些类型的孤立对数正则奇点附近的稳定性结果。作为应用，对于复维2对数正则奇点，我们证明了在孤立对数正则(非对数终端)奇点附近的任何负标量曲率的完备Kähler-Einstein度规平滑渐近地接近双曲几何模型Kähler-Einstein度规。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.