@article{González-Diez_Jones_Torres-Teigell_2014, title={Beauville Surfaces with Abelian Beauville Group}, volume={114}, url={https://www.mscand.dk/article/view/17106}, DOI={10.7146/math.scand.a-17106}, abstractNote={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 $g_{1},g_{2}\ge 2$ by the free action of a finite group $G$. In this paper we study those Beauville surfaces for which $G$ is abelian (so that $G\cong \mathsf{Z}_{n}^{2}$ with $\gcd(n,6)=1$ 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 $\mathsf{Q}$. }, number={2}, journal={MATHEMATICA SCANDINAVICA}, author={González-Diez, G. and Jones, G. A. and Torres-Teigell, D.}, year={2014}, month={May}, pages={191–204} }