Non-planar degenerations and related fundamental groups

Abstract

We present a preliminary investigation of algebraic surfaces that have non-planar degenerations, along with their Galois covers and fundamental groups. Specifically, we investigate the tetrahedron and the double tetrahedron. The resulting fundamental groups indicate that the tetrahedron and the double tetrahedron are in different components of the moduli space of algebraic surfaces.

31 pages, 10 figures