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

  • Received: 04 November 2021 Revised: 14 March 2022 Accepted: 21 March 2022 Published: 26 April 2022
  • 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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