Geometry & Topology

Characteristic varieties of quasi-projective manifolds and orbifolds

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

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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.

Article information

Source
Geom. Topol., Volume 17, Number 1 (2013), 273-309.

Dates
Received: 3 May 2012
Accepted: 22 September 2012
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732524

Digital Object Identifier
doi:10.2140/gt.2013.17.273

Mathematical Reviews number (MathSciNet)
MR3035328

Zentralblatt MATH identifier
1266.32035

Subjects
Primary: 32S20: Global theory of singularities; cohomological properties [See also 14E15] 32S50: Topological aspects: Lefschetz theorems, topological classification, invariants 58K65: Topological invariants
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14H50: Plane and space curves

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

Citation

Artal Bartolo, Enrique; Cogolludo-Agustín, José Ignacio; Matei, Daniel. Characteristic varieties of quasi-projective manifolds and orbifolds. Geom. Topol. 17 (2013), no. 1, 273--309. doi:10.2140/gt.2013.17.273. https://projecteuclid.org/euclid.gt/1513732524


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