Collapsing immortal Kähler-Ricci flows

We consider the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the s...

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Bibliographic Details
Main Authors: Hans-Joachim Hein, Man-Chun Lee, Valentino Tosatti
Format: Article
Language:English
Published: Cambridge University Press 2025-01-01
Series:Forum of Mathematics, Pi
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Online Access:https://www.cambridge.org/core/product/identifier/S2050508625000101/type/journal_article
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Summary:We consider the Kähler-Ricci flow on compact Kähler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian.
ISSN:2050-5086