Characteristic varieties of quasi-projective manifolds and orbifolds

Abstract

The present paper considers the structure of the space of characters of quasi-projective manifolds. Such a space is stratified by the cohomology support loci of rank one local systems called characteristic varieties. The classical structure theorem of characteristic varieties is due to Arapura and it exhibits the positive-dimensional irreducible components as pull-backs obtained from morphisms onto complex curves.

In this paper a different approach is provided, using morphisms onto orbicurves, which accounts also for zero-dimensional components and gives more precise information on the positive-dimensional characteristic varieties. In the course of proving this orbifold version of Arapura’s structure theorem, a gap in his proof is completed. As an illustration of the benefits of the orbifold approach, new obstructions for a group to be the fundamental group of a quasi-projective manifold are obtained.