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

Yang Li; Valentino Tosatti

doi:10.1515/crelle-2023-0025

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

Yang Li, Valentino Tosatti

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Journal	Journal fur die Reine und Angewandte Mathematik
DOIs	https://doi.org/10.1515/crelle-2023-0025
State	Published - 2023

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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abstract = "We study the collapsing of Calabi-Yau metrics and of K{\"a}hler-Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov-Hausdorff limit of the K{\"a}hler-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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AB - 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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On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows

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