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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Bibliographic Details
Published in:American journal of mathematics 2018-06, Vol.140 (3), p.653-698
Main Authors: Tosatti, Valentino, Weinkove, Ben, Yang, Xiaokui
Format: Article
Language:English
Subjects:
Convergence
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Summary: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.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2018.0016