London Algebra Colloquium abstract

Beauville groups and surfaces

Prof. Gareth Jones (Southhampton), 17th January 2013


Beauville surfaces, of current interest to algebraic geometers, are 2-dimensional complex algebraic varieties formed by factoring the cartesian product of two quasiplatonic curves of genus at least 2 by the free action of a finite group, called a Beauville group. A group is a Beauville group if and only if it is a quotient of hyperbolic triangle groups in two essentially different ways. I shall give a survey of recent progress in this topic, such as the result of Guralnick, Malle and others that every non-abelian finite simple group other than A5 is a Beauville group, the description of the automorphism group of a Beauville surface, and the explicit construction, extending examples due to Serre, of arbitrarily large families of Galois conjugate but mutually non-homeomorphic algebraic varieties.