Beauville surfaces with abelian Beauville group

2011/02/22 by Gabino González-Diez, Gareth A. Jones, González-Diez, Gabino +3
Mathematics · #14J29 #14J50 (Primary) 14J25 #20B25 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14J25 #msc:14J29 #msc:14J50 #msc:20B25

paper · pdf · doi:10.48550/arxiv.1102.4552

14 pages. This version contains amended references to related work of Garion and Penegini, who have recently replaced their paper arXiv:0910.5402v1 with arXiv:0910.5402v3 and arXiv:1107.5534, the latter resolving certain discrepancies between their results and ours

arxiv created 2012/03/14 · arxiv updated 2012/03/15

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.

Citations

• New Beauville surfaces and finite simple groups
• Beauville surfaces, moduli spaces and finite groups

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