Beauville surfaces and finite simple groups
Copyright policy )Beauville surfaces and finite simple groups
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.
20 pages
- Indiana University United States
- Max Planck Institute for Mathematics Germany
- Hebrew University of Jerusalem Israel
- DePaul University United States
- Indiana University United States
Surfaces of general type, Generators, relations, and presentations of groups, Ordinary representations and characters, Coverings of curves, fundamental group, Group Theory (math.GR), Simple groups, simple algebraic groups, Linear algebraic groups over arbitrary fields, Mathematics - Algebraic Geometry, finite simple groups, Probabilistic methods in group theory, FOS: Mathematics, Finite simple groups and their classification, Primary 20D06, Secondary 14H30 14J10 20H10, Beauville surfaces, Mathematics - Group Theory, Algebraic Geometry (math.AG), Conjugacy classes for groups, conjugacy classes
Surfaces of general type, Generators, relations, and presentations of groups, Ordinary representations and characters, Coverings of curves, fundamental group, Group Theory (math.GR), Simple groups, simple algebraic groups, Linear algebraic groups over arbitrary fields, Mathematics - Algebraic Geometry, finite simple groups, Probabilistic methods in group theory, FOS: Mathematics, Finite simple groups and their classification, Primary 20D06, Secondary 14H30 14J10 20H10, Beauville surfaces, Mathematics - Group Theory, Algebraic Geometry (math.AG), Conjugacy classes for groups, conjugacy classes
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