منابع مشابه
New 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 کاملCoxeter Groups as Beauville Groups
We generalize earlier work of Fuertes and González-Diez as well as earlier work of Bauer, Catanese and Grunewald by classifying which of the irreducible Coxeter groups are (strongly real) Beauville groups. We also make partial progress on the much more difficult question of which Coxeter groups are Beauville groups in general as well as discussing the related question of which Coxeter groups ca...
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.
متن کاملON BEAUVILLE STRUCTURES FOR PSL(2, q)
We characterize Beauville surfaces of unmixed type with group either PSL(2, p) or PGL(2, p), thus extending previous results of Bauer, Catanese and Grunewald, Fuertes and Jones, and Penegini and the author.
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ژورنال
عنوان ژورنال: Journal of the London Mathematical Society
سال: 2012
ISSN: 0024-6107
DOI: 10.1112/jlms/jdr062