Quotients of fake projective planes

Details Quotients of fake projective planes Quotients of fake projective planes

2008-02-23

arxiv.org/abs/0802.3435v4

Mathematics

Algebraic Geometry

16 pages, with minor change of the exposition

Scientific paper

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 $\bbZ/3\bbZ$, $\bbZ/7\bbZ$, $7:3$, or $(\bbZ/3\bbZ)^2$, 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.

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