Collapsing immortal Kähler-Ricci flows

Hans Joachim Hein; Man Chun Lee; Valentino Tosatti

doi:10.1017/fmp.2025.10

Collapsing immortal Kähler-Ricci flows

Hans Joachim Hein, Man Chun Lee, Valentino Tosatti

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	e18
Journal	Forum of Mathematics, Pi
Volume	13
DOIs	https://doi.org/10.1017/fmp.2025.10
State	Published - May 19 2025

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Statistics and Probability
Mathematical Physics
Geometry and Topology
Discrete Mathematics and Combinatorics

Access to Document

10.1017/fmp.2025.10

Cite this

@article{88055e52c6cf45fa8b443fff23049d78,

title = "Collapsing immortal K{\"a}hler-Ricci flows",

abstract = "We consider the K{\"a}hler-Ricci flow on compact K{\"a}hler 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.",

author = "Hein, {Hans Joachim} and Lee, {Man Chun} and Valentino Tosatti",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2025.",

year = "2025",

month = may,

day = "19",

doi = "10.1017/fmp.2025.10",

language = "English (US)",

volume = "13",

journal = "Forum of Mathematics, Pi",

issn = "2050-5086",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Collapsing immortal Kähler-Ricci flows

AU - Hein, Hans Joachim

AU - Lee, Man Chun

AU - Tosatti, Valentino

PY - 2025/5/19

Y1 - 2025/5/19

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=105005618252&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=105005618252&partnerID=8YFLogxK

U2 - 10.1017/fmp.2025.10

DO - 10.1017/fmp.2025.10

M3 - Article

AN - SCOPUS:105005618252

SN - 2050-5086

VL - 13

JO - Forum of Mathematics, Pi

JF - Forum of Mathematics, Pi

M1 - e18

ER -

Collapsing immortal Kähler-Ricci flows

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this