Beauville Surfaces with Abelian Beauville Group
نویسندگان
چکیده
منابع مشابه
Beauville Surfaces and Probabilistic Group Theory
A Beauville surface is a complex algebraic surface that can be presented as a quotient of a product of two curves by a suitable action of a finite group. Bauer, Catanese and Grunewald have been able to intrinsically characterize the groups appearing in minimal presentations of Beauville surfaces in terms of the existence of a so-called ”Beauville structure“. They conjectured that all finite sim...
متن کاملNew Beauville Surfaces and Finite Simple Groups
In this paper we construct new Beauville surfaces with group either PSL(2, p), or belonging to some other families of finite simple groups of Lie type of low Lie rank, or an alternating group, or a symmetric group, proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on probabilistic group theoretical results of Liebeck and Shalev, on classical results of Macbeath and on recen...
متن کاملBeauville Surfaces and Finite Simple Groups
A Beauville surface is a rigid complex surface of the form (C1 × C2)/G, where C1 and C2 are non-singular, projective, higher genus curves, and G is a finite group acting freely on the product. Bauer, Catanese, and Grunewald conjectured that every finite simple group G, with the exception of A5, gives rise to such a surface. We prove that this is so for almost all finite simple groups (i.e., wit...
متن کاملBeauville Surfaces, Moduli Spaces and Finite Groups
In this paper we give the asymptotic growth of the number of connected components of the moduli space of surfaces of general type corresponding to certain families of Beauville surfaces with group either PSL(2, p), or an alternating group, or a symmetric group or an abelian group. We moreover extend these results to regular surfaces isogenous to a higher product of curves.
متن کاملBeauville p-groups: a survey
Beauville surfaces are a class of complex surfaces defined by letting a finite group G act on a product of Riemann surfaces. These surfaces possess many attractive geometric properties several of which are dictated by properties of the group G. In this survey we discuss the p-groups that may be used in this way. En route we discuss several open problems, questions and conjectures.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 2014
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-17106