Kähler–Einstein metrics near an isolated log-canonical singularity

IF 1.2 1区数学 Q1 MATHEMATICS

Journal fur die Reine und Angewandte Mathematik 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

Journal fur die Reine und Angewandte Mathematik 数学-数学

CiteScore

2.50

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of Crelle"s Journal. In the almost 180 years of its existence, Crelle"s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals. It belongs to the very top mathematics periodicals, as listed in ISI"s Journal Citation Report.