Characteristic varieties of quasi-projective manifolds and orbifolds. (English) Zbl 1266.32035

Bartolo, Enrique Artal; Cogolludo-Agustín, José Ignacio; Matei, Daniel

Geom. Topol. 17, No. 1, 273-309 (2013).

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.

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

Keywords:

quasi-projective manifolds; characteristic varieties; orbicurves

Citations:

Zbl 0923.14010

References:

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