Free quotients of fundamental groups of smooth quasi-projective varieties

Abstract

We consider the structure of classes of curves on a projective simply connected surface for which fundamental groups of the complements admit free quotients having rank greater than one with irreducible components belonging to a selected subset the effective cone of the surface. In particular we show a finiteness result for such classes if the ranks of free quotients of the fundamental groups with components in the subset of effective cone are sufficiently large.

arXiv commentSubstantial revision. Final version to appear in Proc. Edinburgh Mathematical Society