Characteristically simple Beauville groups, I: cartesian powers of alternating groups

2013/04/19 by Gareth A. Jones, Jones, Gareth A.
Mathematics · #14J25 #20D05 (primary) #30F10 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1304.5444

openalex publication_date 2013/04/19 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

A Beauville surface (of unmixed type) is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the product, where G preserves the two curves and their quotients by G are isomorphic to the projective line, ramified over three points. Such a group G is called a Beauville group. We show that if a characteristically simple group G is a cartesian power of a finite simple alternating group, then G is a Beauville group if and only if it has two generators and is not isomorphic to A₅.

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