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Characteristic varieties of quasi-projective manifolds and orbifolds. (English) Zbl 1266.32035
Summary: 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 D. Arapura [J. Algebr. Geom. 6, No. 3, 563–597 (1997; Zbl 0923.14010)] 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.
Reviewer: Reviewer (Berlin)

MSC:
32S20 Global theory of complex singularities; cohomological properties
32S50 Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants
58K65 Topological invariants on manifolds
14B05 Singularities in algebraic geometry
14H30 Coverings of curves, fundamental group
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