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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157146This 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 pagesAlgebraic Geometry14J10; 14J25The fundamental group of Galois cover of the surface ${\mathbb T} \times {\mathbb T}$text