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.
Citation: Yan Li, Gang Tian, Xiaohua Zhu. Singular Kähler-Einstein metrics on Q-Fano compactifications of Lie groups[J]. Mathematics in Engineering, 2023, 5(2): 1-43. doi: 10.3934/mine.2023028
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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.
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