Collapsing immortal Kähler-Ricci flows
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909616406790144 |
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| author | Hein, Hans-Joachim Lee, Man-Chun Tosatti, Valentino |
| author_facet | Hein, Hans-Joachim Lee, Man-Chun Tosatti, Valentino |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04208 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Collapsing immortal Kähler-Ricci flows Hein, Hans-Joachim Lee, Man-Chun Tosatti, Valentino Differential Geometry Analysis of PDEs 53E30, 32Q15, 32W20, 35K96, 58J35 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. |
| title | Collapsing immortal Kähler-Ricci flows |
| topic | Differential Geometry Analysis of PDEs 53E30, 32Q15, 32W20, 35K96, 58J35 |
| url | https://arxiv.org/abs/2405.04208 |