Beauville Surfaces with Abelian Beauville Group

  • G. González-Diez
  • G. A. Jones
  • D. Torres-Teigell

Abstract

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 $\mathsf{Q}$.
Published
2014-05-06
How to Cite
González-Diez, G., Jones, G. A., & Torres-Teigell, D. (2014). Beauville Surfaces with Abelian Beauville Group. MATHEMATICA SCANDINAVICA, 114(2), 191-204. https://doi.org/10.7146/math.scand.a-17106
Section
Articles