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- Title
On the collapsing of Calabi–Yau manifolds and Kähler–Ricci flows.
- Authors
Li, Yang; Tosatti, Valentino
- 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.
- Subjects
CALABI-Yau manifolds; HAUSDORFF measures; METRIC geometry
- Publication
Journal für die Reine und Angewandte Mathematik, 2023, Vol 2023, Issue 800, p155
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2023-0025