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

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

引用次数: 1

Abstract

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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关于Calabi-Yau流形和Kähler-Ricci流的坍缩

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。

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

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