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

Abstract

In this paper, we prove an existence result for Kähler-Einstein metrics on $\mathbb{Q}$-Fano compactifications of Lie groups. As an application, we classify $\mathbb{Q}$-Fano compactifications of $S{O}_4(\mathbb{C})$ which admit a Kähler-Einstein metric with the same volume as that of a smooth Fano compactification of $S{O}_4(\mathbb{C})$.

Comments are welcome. 38 pages, 6 figures and 2 tables