The Coxeter quotient of the fundamental group of a Galois cover of T \times T

Details The Coxeter quotient of the fundamental group of a Galois cover of T \times T The Coxeter quotient of the fundamental group of a Galois cover of T \times T

2004-04-26

arxiv.org/abs/math/0404459v2

Mathematics

Algebraic Geometry

25 pp

Scientific paper

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 $\C\P^2$. 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.

Affiliated with

Also associated with

No associations

Rating

The Coxeter quotient of the fundamental group of a Galois cover of T \times T does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Coxeter quotient of the fundamental group of a Galois cover of T \times T, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Coxeter quotient of the fundamental group of a Galois cover of T \times T will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-630755