On the collapsing of Calabi–Yau manifolds and Kähler–Ricci flows
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10.1515_crelle-2023-0025.pdf
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Author(s)
Yang Li
Valentino Tosatti
Date Issued
June 1, 2023
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter GmbH
Citation
Li, Yang and Tosatti, Valentino. "On the collapsing of Calabi–Yau manifolds and Kähler–Ricci flows" Journal für die reine und angewandte Mathematik (Crelles Journal), vol. 2023, no. 800, 2023, pp. 155-192.
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1515/crelle-2023-0025
