TY - JOUR
AU - González-Diez, G.
AU - Jones, G. A.
AU - Torres-Teigell, D.
PY - 2014/05/06
Y2 - 2024/08/03
TI - Beauville Surfaces with Abelian Beauville Group
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 114
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-17106
UR - https://www.mscand.dk/article/view/17106
SP - 191-204
AB - 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 $\mathsf{Q}$.
ER -