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.
Keywords
characteristic varieties, local systems, cohomology jumping
loci, cohomology with twisted coefficients,
quasi-projective groups, orbicurves, orbifolds