TY - JOUR
T1 - Beauville surfaces and finite simple groups
AU - Garion, Shelly
AU - Larsen, Michael
AU - Lubotzky, Alexander
PY - 2012/5
Y1 - 2012/5
N2 - A Beauville surface is a rigid complex surface of the form (C 1 × C 2)/G, where C 1 and C 2 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 A 5, 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.
AB - A Beauville surface is a rigid complex surface of the form (C 1 × C 2)/G, where C 1 and C 2 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 A 5, 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.
UR - http://www.scopus.com/inward/record.url?scp=84861486802&partnerID=8YFLogxK
U2 - 10.1515/CRELLE.2011.117
DO - 10.1515/CRELLE.2011.117
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AN - SCOPUS:84861486802
SN - 0075-4102
SP - 225
EP - 243
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 666
ER -