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arXiv · 2107.00836

On the collapsing of Calabi-Yau manifolds and K\"ahler-Ricci flows

Yang Li·Valentino Tosatti
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Abstract

We study the collapsing of Calabi-Yau metrics and of Kahler-Ricci flows on fiber spaces where the base is smooth. We identify the collapsed Gromov-Hausdorff limit of the Kahler-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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BibTeXRIS

Yang Li, Valentino Tosatti. 2021-07-02. On the collapsing of Calabi-Yau manifolds and K\"ahler-Ricci flows. https://doi.org/10.1515/crelle-2023-0025

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