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.
New Beauville surfaces and finite simple groups / S. Garion, M. Penegini. - In: MANUSCRIPTA MATHEMATICA. - ISSN 0025-2611. - 142:3-4(2013), pp. 391-408.
New Beauville surfaces and finite simple groups
M. Penegini
2013
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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