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Groups in Algebraic Geometry.

Quotients of fake projective planes

speaker: JongHae Keum (KIAS (Korea Institute for Advanced Study))

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 $Z3Z$, $Z7Z$, $7:3$, or $(Z3Z)^2$, 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 lecture we classify all possible structures of the quotient surface $XG$ and its minimal resolution.

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