关于Calabi-Yau流形和Kähler-Ricci流的坍缩

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-07-02 DOI:10.1515/crelle-2023-0025

Yang Li, Valentino Tosatti

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引用次数: 1

摘要

研究了基底光滑的光纤空间上Calabi-Yau度量和Kähler-Ricci流的坍缩。当判别轨迹的分型部分有简单的正交点时，我们确定了Kähler-Ricci流的崩塌Gromov-Hausdorff极限。在这两种情况下，我们也得到了Cheeger-Colding奇异集的实余维-2 Hausdorff测度的显界，并从双几何中找到了一个充分条件来理解极限测度在基上的度量行为。

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On the collapsing of Calabi–Yau manifolds and Kähler–Ricci flows

Abstract We study the collapsing of Calabi–Yau metrics and of Kähler–Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov–Hausdorff limit of the Kähler–Ricci flow when the divisorial part of the discriminant locus has simple normal crossings. In either setting, we also obtain an explicit bound for the real codimension-2 Hausdorff measure of the Cheeger–Colding singular set and identify a sufficient condition from birational geometry to understand the metric behavior of the limiting metric on the base.

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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.