The Coxeter quotient of the fundamental group of a Galois cover of T \times T
Abstract
Let $X$ be the surface $\T\times\T$ where $\T$ is the complex torus. This paper is the third in a series, studying the fundamental group of the Galois cover of $X$ \wrt a generic projection onto $\C¶^2$. Van Kampen Theorem gives a presentation of the fundamental group of the complement of the branch curve, with 54 generators and more than 2000 relations. Here we introduce a certain natural quotient (obtained by identifying pairs of generators), prove it is a quotient of a Coxeter group related to the degeneration of $X$, and show that this quotient is virtually nilpotent.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2004
 arXiv:
 arXiv:math/0404459
 Bibcode:
 2004math......4459M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Group Theory;
 14J29
 EPrint:
 25 pp