Singular Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups†

Yan Li; Gang Tian; Xiaohua Zhu

doi:10.3934/mine.2023028

Singular Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups†

Yan Li, Gang Tian, Xiaohua Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Peking University

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

3 Citations (Scopus)

Abstract

In this paper, we prove an existence result for Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a fine condition. As an application, we prove that there is no Q-Fano SO₄(C)-compactification which admits a Ka¨hler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO₄(C)-compactification.

Original language	English
Pages (from-to)	1-43
Number of pages	43
Journal	Mathematical Foundations of Computing
Volume	5
Issue number	2
DOIs	https://doi.org/10.3934/mine.2023028
Publication status	Published - 2022

Keywords

K-stability
Ka¨hler-Einstein metrics
Q-Fano compactifications of Lie groups
reduced Ding functional
variation method

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10.3934/mine.2023028

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abstract = "In this paper, we prove an existence result for Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a fine condition. As an application, we prove that there is no Q-Fano SO4(C)-compactification which admits a Ka¨hler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO4(C)-compactification.",

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AB - In this paper, we prove an existence result for Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a fine condition. As an application, we prove that there is no Q-Fano SO4(C)-compactification which admits a Ka¨hler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO4(C)-compactification.

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KW - Ka¨hler-Einstein metrics

KW - Q-Fano compactifications of Lie groups

KW - reduced Ding functional

KW - variation method

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Singular Ka¨hler-Einstein metrics on Q-Fano compactifications of Lie groups†

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Keywords

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