2024/05/07 by Hans‐Joachim Hein, Man-Chun Lee, Hein, Hans-Joachim +3
Mathematics · #32Q15 #32W20 #35K96 #53E30 #58J35 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2405.04208
openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.