The fundamental group of Galois cover of the surface $\mathbb{T}\times \mathbb{T}$

Abstract

This is the final paper in a series of four, concerning the surface $T\times T$ embedded in ${\mathbb{CP}}^8$, where $T$ is a the one dimensional torus. In this paper we compute the fundamental group of the Galois cover of the surface with respect to a generic projection onto ${\mathbb{CP}}^2$, and show that it is nilpotent of class 3. This is the first time such a group is presented as the fundamental group of a Galois cover of a surface.

30 pages