Beauville surfaces and finite groups

Abstract

Extending results of Bauer, Catanese and Grunewald, and of Fuertes and González-Diez, we show that Beauville surfaces of unmixed type can be obtained from the groups L_2(q) and SL_2(q) for all prime powers q>5, and the Suzuki groups Sz(2^e) and the Ree groups R(3^e) for all odd e>1. We also show that L_2(q) and SL_2(q) admit strongly real Beauville structures, yielding real Beauville surfaces, if and only if q>5.

18 pages. Second version acknowledges overlap with work of Garion and Penegini (arXiv:0910.5402) and corrects statements of results about linear groups over small fields