A topological construction of families of Galois covers of the line

Abstract

We describe a new construction of families of Galois coverings of the line using basic properties of configuration spaces, covering theory, and the Grauert–Remmert extension theorem. Our construction provides an alternative to a previous construction due to González-Díez and Harvey (which uses Teichmüller theory and Fuchsian groups) and, in the case the Galois group is nonabelian, corrects an inaccuracy therein. In the opposite case where the Galois group has trivial center, we recover some results due to Fried and Völklein.