Quotients of fake projective planes

Abstract

Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to $\mathbb{Z}∕3\mathbb{Z}$, $\mathbb{Z}∕7\mathbb{Z}$, 7:3 or ${\left(\mathbb{Z}∕3\mathbb{Z}\right)}^2$, where 7:3 is the unique nonabelian group of order 21.

Let $G$ be a group of automorphisms of a fake projective plane $X$. In this paper we classify all possible structures of the quotient surface $X∕G$ and its minimal resolution.