Automorphism groups of Beauville surfaces

作者：Jones Gareth A^*

来源：Journal of Group Theory, 2013, 16(3): 353-381.

DOI：10.1515/jgt-2012-0049

A Beauville surface of unmixed type is a complex algebraic surface which is the quotient of the product of two curves of genus at least 2 by a finite group G acting freely on the product, where G preserves the two curves and their quotients by G are isomorphic to the projective line, ramified over three points. We show that the automorphism group A of such a surface has an abelian normal subgroup I isomorphic to the centre of G, induced by pairs of elements of G acting compatibly on the curves (a result obtained independently by Fuertes and Gonzalez-Diez). Results of Singerman on inclusions between triangle groups imply that A/I is isomorphic to a subgroup of the wreath product S-3 (sic) S-2, so A is a finite solvable group. Using constructions based on Lucchini%26apos;s work on generators of special linear groups, we show that every finite abelian group can arise as I, even if one restricts the index \A : I\ to the extreme values 1 or 72.

• 出版日期2013-5