Characteristic varieties of quasi-projective manifolds and orbifolds

TL;DR

This paper characterizes the structure of characteristic varieties of quasi-projective manifolds, showing they are either pull-backs from orbifolds or torsion points, providing new insights into their geometric and topological properties.

Contribution

It establishes a classification of irreducible components of characteristic varieties, linking them to orbifolds and torsion points, and derives obstructions for fundamental groups of such manifolds.

Findings

Irreducible components are pull-backs or torsion points.

Zero-dimensional components are torsion.

Provides obstructions for fundamental groups of quasi-projective manifolds.

Abstract

We prove that the irreducible components of the characteristic varieties of quasi-projective manifolds are either pull-backs of such components for orbifolds, or torsion points. This gives an interpretation for the so-called \emph{translated} components of the characteristic varieties, and shows that the zero-dimensional components are indeed torsion. The main result is used to derive further obstructions for a group to be the fundamental group of a quasi-projective manifold.