Singular Kähler-Einstein metrics on $ \mathbb Q $-Fano compactifications of Lie groups-Reference-Cited by-同舟云学术

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

Published:2022 Issue:2 Volume:5 Page:1-43
ISSN:2640-3501
Container-title:Mathematics in Engineering
language:
Short-container-title:MINE

Author:

Li Yan¹,Tian Gang²,Zhu Xiaohua²

Affiliation:

1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

2. Beijing International Centre of Mathematical Research and School of Mathematical Science, Peking University, Beijing 100871, China

Abstract

<abstract><p>In this paper, we prove an existence result for Kähler-Einstein metrics on $ \mathbb Q $-Fano compactifications of Lie groups by the variational method, provided their moment polytopes satisfy a <italic>fine</italic> condition. As an application, we prove that there is no $ \mathbb Q $-Fano $ {\rm SO}_4(\mathbb C) $-compactification which admits a Kähler-Einstein metric with the same volume as that of a smooth K-unstable Fano $ {\rm SO}_4(\mathbb C) $-compactification.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Mathematical Physics,Analysis

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