Quotients of fake projective planes

Keum, JongHae¹

¹ School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, Korea

Geometry & topology, Tome 12 (2008) no. 4, pp. 2497-2515.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.2497

Keywords: fake projective plane, surface of general type, Dolgachev surface, properly elliptic surface, fundamental group

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