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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Cambridge University Press
2025-01-01
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| 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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| author | Hans-Joachim Hein Man-Chun Lee Valentino Tosatti |
| author_facet | Hans-Joachim Hein Man-Chun Lee Valentino Tosatti |
| author_sort | Hans-Joachim Hein |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0e8f1b34dba04f3b93cbf5f6ec4c29da |
| institution | OA Journals |
| issn | 2050-5086 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Pi |
| spelling | doaj-art-0e8f1b34dba04f3b93cbf5f6ec4c29da2025-08-20T01:54:57ZengCambridge University PressForum of Mathematics, Pi2050-50862025-01-011310.1017/fmp.2025.10Collapsing immortal Kähler-Ricci flowsHans-Joachim Hein0https://orcid.org/0000-0002-3719-9549Man-Chun Lee1https://orcid.org/0000-0002-4663-6149Valentino Tosatti2Mathematisches Institut, Universität Münster, Einsteinstraße 62, Münster, 48149, Germany; E-mail:Department of Mathematics, The Chinese University of Hong Kong, Lady Shaw Building, Shatin, N.T., 999077, Hong Kong; E-mail:Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, USAWe 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.https://www.cambridge.org/core/product/identifier/S2050508625000101/type/journal_article53E3032Q1535K9658J3532W20 |
| spellingShingle | Hans-Joachim Hein Man-Chun Lee Valentino Tosatti Collapsing immortal Kähler-Ricci flows Forum of Mathematics, Pi 53E30 32Q15 35K96 58J35 32W20 |
| title | Collapsing immortal Kähler-Ricci flows |
| title_full | Collapsing immortal Kähler-Ricci flows |
| title_fullStr | Collapsing immortal Kähler-Ricci flows |
| title_full_unstemmed | Collapsing immortal Kähler-Ricci flows |
| title_short | Collapsing immortal Kähler-Ricci flows |
| title_sort | collapsing immortal kahler ricci flows |
| topic | 53E30 32Q15 35K96 58J35 32W20 |
| url | https://www.cambridge.org/core/product/identifier/S2050508625000101/type/journal_article |
| work_keys_str_mv | AT hansjoachimhein collapsingimmortalkahlerricciflows AT manchunlee collapsingimmortalkahlerricciflows AT valentinotosatti collapsingimmortalkahlerricciflows |