Beauville surfaces and finite simple groups

Details Beauville surfaces and finite simple groups Beauville surfaces and finite simple groups

2010-05-13

arxiv.org/abs/1005.2316v1

Mathematics

Group Theory

20 pages

Scientific paper

10.1515/CRELLE.2011.117

A Beauville surface is a rigid complex surface of the form (C1 x 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., with at most finitely many exceptions). The proof makes use of the structure theory of finite simple groups, probability theory, and character estimates.

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