Beauville Surfaces and Triangle Groups
Dr. P. Vanchinathan
Chennai Mathematical Institute.
20-10-10

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Abstract

12.00 noon
When a product of two smooth complex projective curves $C_1,C_2$ of genus $> 1$ admitting a free action of a finite group, having the property that the quotient surface is rigid there are interesting consequences.

Such quotients, called Beauville surfaces by Catanese, are defined over number fields, and lead to representations of the absolute Galois group of Q, $Gal( \bar{Q}/Q )$. In the viewpoint of Bauer, Catanese and Grunewald, they are more convenient than dessin d'enfants.

Existence of such an action of a finite group ties up with some classical group-theoretic questions and conjectures.

An overview of the work of these authors and the work of S.Garion, M. Larsen, and A. Lubotsky announced in arXiv's earlier this year will be presented.