New Beauville surfaces and finite simple groups

2009/10/28 by Shelly Garion, Garion, Shelly, Matteo Penegini +1 · 2 citations
Mathematics · #14J10 #14J29 #20D06 #20H10 #30F99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14J10 #msc:14J29 #msc:20D06 #msc:20H10 #msc:30F99

paper · pdf · doi:10.48550/arxiv.0910.5402

v4: 18 pages. Final version, to appear in Manuscripta Math

arxiv created 2012/11/29 · arxiv updated 2012/11/30

Abstract

In this paper we construct new Beauville surfaces with group either \PSL(2,p^e), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recent results of Marion.

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