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Research Article | Open Access

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

Yan Li1, Gang Tian2, Xiaohua Zhu2( )
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China
Beijing International Centre of Mathematical Research and School of Mathematical Science, Peking University, Beijing 100871, China
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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 S O 4 ( C )-compactification which admits a Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano S O 4 ( C )-compactification.

Keywords

Kähler-Einstein metricsQ-Fano compactifications of Lie groupsvariation methodreduced Ding functionalK-stability

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Mathematics in Engineering
Volume 5 Issue 2,
April 2023
Pages 1-43
DOI: 10.3934/mine.2023028

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Cite this article:
Li Y, Tian G, Zhu X. Singular Kähler-Einstein metrics on Q -Fano compactifications of Lie groups. Mathematics in Engineering, 2023, 5(2): 1-43. https://doi.org/10.3934/mine.2023028

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Received: 04 November 2021
Revised: 14 March 2022
Accepted: 21 March 2022
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)