Quotients of fake projective planes

Keum, JongHae

doi:10.2140/gt.2008.12.2497

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Quotients of fake projective planes

JongHae Keum

Geometry & Topology 12 (2008) 2497–2515

DOI: 10.2140/gt.2008.12.2497

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 $ℤ ∕ 3 ℤ$ , $ℤ ∕ 7 ℤ$ , 7:3 or ${(ℤ ∕ 3 ℤ)}^{2}$ , 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

Mathematical Subject Classification 2000

Primary: 14J29

Secondary: 14J27

References

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

Volume 12, issue 4 (2008)