The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits

Valentino Tosatti, Ben Weinkove, Xiaokui Yang

Published 2014-08-01, updated 2017-01-11Version 2

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.