Quotients of fake projective planes

By JongHae Keum. 2008

56 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/ce8203f7235e3e72b47fc5ed83830ad138015af4

Citations in the corpus

• Enumeration of the 50 fake projective planes = Énumération des 50 faux plans projectifs (2010, unknown): “…with a presentation of each of the 28 Γ ’s, we are able to list not only the subgroups Π of index N , but also the subgroups H such that Π < H (cid:2) ¯ Γ = C 2 = C 2 = (cid:10) (cid:11) the case Π (cid:12) H , Keum [6] obtained much information about the possible M from general considerations.”