Beauville surfaces with abelian Beauville group

2011/02/22 by González-Diez, Gabino, Jones, Gareth A., Torres-Teigell, David
#14J29 #14J50 (Primary) 14J25 #20B25 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1102.4552

Abstract

A Beauville surface is a rigid surface of general type arising as a quotient of a product of curves C₁, C₂ of genera g₁,g₂≥ 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≅ ℤ_n² 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 ℚ.

Related

• Recent work on Beauville surfaces, structures and groups
• Automorphism groups of Beauville surfaces
• Beauville surfaces and finite groups
• Some new surfaces with p_g = q = 0
• Generalised Beauville Groups