Symmetric and Kähler--Einstein Fano polygons

Abstract

We investigate \emph{singular} symmetric and Kähler--Einstein Fano polytopes. More precisely, we show that every symmetric Fano polytope is Kähler--Einstein generalizing the work by Batyrev and Selivanova, and study the automorphism groups of symmetric and Kähler--Einstein Fano polygons in detail. In particular, every finte subgroup of $G{L}_2(\mathbb{Z})$ is an automorphism group of a Kähler--Einstein Fano polygon.

Final version, to appear in Proc. Amer. Math. Soc