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

IF 1.2 1区 数学 Q1 MATHEMATICS
Yang Li, Valentino Tosatti
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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.
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
CiteScore
2.50
自引率
6.70%
发文量
97
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.
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