Geometry of twisted K\"ahler-Einstein metrics and collapsing
Differential Geometry
2020-11-24 v2 Algebraic Geometry
Metric Geometry
Abstract
We prove that the twisted Kahler-Einstein metrics that arise on the base of certain holomorphic fiber space with Calabi-Yau fibers have conical-type singularities along the discriminant locus. These fiber spaces arise naturally when studying the collapsing of Ricci-flat Kahler metrics on Calabi-Yau manifolds, and of the Kahler-Ricci flow on compact Kahler manifolds with semiample canonical bundle and intermediate Kodaira dimension. Our results allow us to understand their collapsed Gromov-Hausdorff limits when the base is smooth and the discriminant has simple normal crossings.
Keywords
Cite
@article{arxiv.1911.07315,
title = {Geometry of twisted K\"ahler-Einstein metrics and collapsing},
author = {Mark Gross and Valentino Tosatti and Yuguang Zhang},
journal= {arXiv preprint arXiv:1911.07315},
year = {2020}
}
Comments
39 pages; final version to appear in Comm Math Phys