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Collapsing immortal K\"ahler-Ricci flows

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arxiv 2405.04208 v2 pith:2RUIIYC7 submitted 2024-05-07 math.DG math.AP

Collapsing immortal K\"ahler-Ricci flows

Hans-Joachim Hein , Man-Chun Lee , Valentino Tosatti This is my paper
classification math.DG math.AP
keywords ahler-riccicanonicalcollapsingflowmetricsahlerasymptoticauthors
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We consider the K\"ahler-Ricci flow on compact K\"ahler 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.

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