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 $(\mathbb{Z}/3\mathbb{Z}{)}^2$, where $7:3$ is the unique non-abelian 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.

16 pages, with minor change of the exposition

References in corpus (2)

• A simply connected surface of general type with p_g=0 and K^2=2
• Fake projective planes

Cited by in corpus (6)

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• Explicit equations of a fake projective plane
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• On the orders of periodic diffeomorphisms of 4-manifolds
• Automorphisms and quotients of quaternionic fake quadrics
• Milnor-Wood inequality for klt varieties of general type and uniformization