On the collapsing of Calabi-Yau manifolds and Kähler-Ricci flows
arXiv:2107.00836 · doi:10.1515/crelle-2023-0025
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.
37 pages; final version to appear in J. Reine Angew. Math; typos fixed