The Kähler-Ricci flow on log canonical pairs of general type

Chang Li; Liangming Shen; Tao Zheng

doi:10.1016/j.jfa.2023.109984

The Kähler-Ricci flow on log canonical pairs of general type

Chang Li, Liangming Shen, Tao Zheng^*

^*Corresponding author for this work

School of Mathematics and Statistics

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

Abstract

We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L^∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of K_X+Δ if the log canonical pair is of general type.

Original language	English
Article number	109984
Journal	Journal of Functional Analysis
Volume	285
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2023.109984
Publication status	Published - 15 Aug 2023

Keywords

Big and nef
Kähler-Ricci flow
Log canonical pair

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10.1016/j.jfa.2023.109984

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abstract = "We generalize existence results of the K{\"a}hler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the K{\"a}hler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized K{\"a}hler-Ricci flow converges to the singular K{\"a}hler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.",

keywords = "Big and nef, K{\"a}hler-Ricci flow, Log canonical pair",

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AU - Shen, Liangming

AU - Zheng, Tao

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N2 - We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.

AB - We generalize existence results of the Kähler-Ricci flow in [10] to log canonical pairs. We show that if the initial data is in L∞ the Kähler-Ricci flow simultaneously develops the conical and cusp singularities along the regular part of the corresponding pair divisors. Furthermore we could show that the normalized Kähler-Ricci flow converges to the singular Kähler-Einstein metric inside the ample locus of KX+Δ if the log canonical pair is of general type.

KW - Big and nef

KW - Kähler-Ricci flow

KW - Log canonical pair

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DO - 10.1016/j.jfa.2023.109984

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JO - Journal of Functional Analysis

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M1 - 109984

ER -

The Kähler-Ricci flow on log canonical pairs of general type

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Keywords

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