Fundamental groups of Galois covers of degree 5 surfaces

Abstract

Let X be an algebraic surface of degree 5, which is considered a branch cover of CP2 with respect to a generic projection. The surface has a natural Galois cover with Galois group S5 . In this paper, we deal with the fundamental groups of Galois covers of degree 5 surfaces that degenerate to nice plane arrangements; each of them is a union of five planes such that no three planes meet in a line