Singular Kähler-Einstein metrics on Q-Fano compactifications of Lie groups

Yan Li; Gang Tian; Xiaohua Zhu

doi:10.3934/mine.2023028

Singular Kähler-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

1 Citation (Scopus)

Abstract

In this paper, we prove an existence result for Kähler-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 Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO₄(C)compactification.

Original language	English
Journal	Mathematics In Engineering
Volume	5
Issue number	2
DOIs	https://doi.org/10.3934/mine.2023028
Publication status	Published - 2022

Keywords

K-stability
Kähler-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 K{\"a}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 K{\"a}hler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO4(C)compactification.",

keywords = "K-stability, K{\"a}hler-Einstein metrics, Q-Fano compactifications of Lie groups, reduced Ding functional, variation method",

author = "Yan Li and Gang Tian and Xiaohua Zhu",

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AU - Tian, Gang

AU - Zhu, Xiaohua

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N2 - In this paper, we prove an existence result for Kähler-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 Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO4(C)compactification.

AB - In this paper, we prove an existence result for Kähler-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 Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano SO4(C)compactification.

KW - K-stability

KW - Kähler-Einstein metrics

KW - Q-Fano compactifications of Lie groups

KW - reduced Ding functional

KW - variation method

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VL - 5

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JF - Mathematics In Engineering

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ER -

Singular Kähler-Einstein metrics on Q-Fano compactifications of Lie groups

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Keywords

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