Beauville Surfaces with Abelian Beauville Group - González-Diez, G.; Jones, G. A.; Torres-Teigell, D. (MATHEMATICA SCANDINAVICA, 2014)
A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves C_1, C_2 of genera g_1,g_22 by the free action of a finite group G. In this paper we study those Beauville surfaces for which G is abelian (so that GZ_n^2 with (n,6)=1 by a result of Catanese). For each such n we are able to describe all such surfaces, give a formula for the number of their isomorphism classes and identify their possible automorphism groups. This explicit description also allows us to observe that such surfaces are all defined over Q.