We prove that if a finite group acts freely on a product of two curves so that the quotient is a Beauville surface then and are both non hyperelliptic curves of genus ; the lowest bound being achieved when is the Fermat curve of genus and . We also determine the possible values of the genera of and when equals , or any abelian group. Finally, we produce examples of Beauville surfaces in which is a -group with .
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Yolanda Fuertes, Gabino González-Diez, Andrei Jaikin-Zapirain, On Beauville surfaces. Groups Geom. Dyn. 5 (2011), no. 1, pp. 107–119DOI 10.4171/GGD/117