#### Volume 12, issue 4 (2008)

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Quotients of fake projective planes

### JongHae Keum

Geometry & Topology 12 (2008) 2497–2515
##### 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 $ℤ∕3ℤ$, $ℤ∕7ℤ$, 7:3 or ${\left(ℤ∕3ℤ\right)}^{2}$, 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.

##### Keywords
fake projective plane, surface of general type, Dolgachev surface, properly elliptic surface, fundamental group
Primary: 14J29
Secondary: 14J27
##### Publication
Received: 3 March 2008
Revised: 14 June 2008
Accepted: 5 June 2008
Published: 8 October 2008
Proposed: Ron Stern
Seconded: Ron Fintushel, Walter Neumann
##### Authors
 JongHae Keum School of Mathematics Korea Institute for Advanced Study Seoul 130-722 Korea