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 ⩾ 3 . We also show that L 2 ( q ) and SL 2 ( q ) admit strongly real Beauville structures, yielding real Beauville surfaces, for all q > 5 .