THE KÄHLER-RICCI FLOW, RICCI-FLAT METRICS AND COLLAPSING LIMITS

We investigate the Kähler-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 Kähler metrics. This...

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Published in:American journal of mathematics 2018-06, Vol.140 (3), p.653-698
Main Authors: Tosatti, Valentino, Weinkove, Ben, Yang, Xiaokui
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Language:English
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Convergence
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Yang, Xiaokui
description We investigate the Kähler-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 Kähler metrics. This strengthens previous work of Song-Tian and others. We obtain analogous results for degenerations of Ricci-flat Kähler metrics.
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subjects Convergence
title THE KÄHLER-RICCI FLOW, RICCI-FLAT METRICS AND COLLAPSING LIMITS
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