Beauville Surfaces with Abelian Beauville Group

Autores: Gabino González Díez , Gareth A. Jones, D. Torres
Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 114, Nº 2, 2014, págs. 191-204
Idioma: inglés
DOI: 10.7146/math.scand.a-17106
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Resumen
- 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 $\mathsf{Q}$.