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.
arXiv comment37 pages; final version to appear in J. Reine Angew. Math; typos fixed
References in corpus (15)
- Notes on Perelman's papers
- Adiabatic limits of Ricci-flat Kahler metrics
- The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits
- Gromov-Hausdorff collapsing of Calabi-Yau manifolds
- Collapsing of abelian fibred Calabi-Yau manifolds
- KAWA lecture notes on the Kähler-Ricci flow
- The Collapsing Rate of the Kähler-Ricci Flow with Regular Infinite Time Singularity
- Remarks on the collapsing of torus fibered Calabi-Yau manifolds
- Higher-order estimates for collapsing Calabi-Yau metrics
- Finite time collapsing of the Kähler-Ricci flow on threefolds
- Collapsing hyperkähler manifolds
- Calabi-Yau manifolds and their degenerations
- Collapsing Calabi-Yau manifolds
- Geometry of twisted Kähler-Einstein metrics and collapsing
- A travel guide to the canonical bundle formula