The K\"ahler-Ricci flow, Ricci-flat metrics and collapsing limits
Differential Geometry
2018-05-17 v2
Abstract
We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled metrics on the fibers converge to Ricci-flat Kahler metrics. This strengthens previous work of Song-Tian and others. We obtain analogous results for degenerations of Ricci-flat Kahler metrics.
Keywords
Cite
@article{arxiv.1408.0161,
title = {The K\"ahler-Ricci flow, Ricci-flat metrics and collapsing limits},
author = {Valentino Tosatti and Ben Weinkove and Xiaokui Yang},
journal= {arXiv preprint arXiv:1408.0161},
year = {2018}
}
Comments
42 pages, final version to appear in Amer. J. Math