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

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>

Topics & Concepts