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Characteristic varieties of quasi-projective manifolds and orbifolds

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

Geometry & Topology 17 (2013) 273–309

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.

characteristic varieties, local systems, cohomology jumping loci, cohomology with twisted coefficients, quasi-projective groups, orbicurves, orbifolds
Mathematical Subject Classification 2010
Primary: 32S20, 32S50, 58K65
Secondary: 14B05, 14H30, 14H50
Received: 3 May 2012
Accepted: 22 September 2012
Published: 7 March 2013
Proposed: Lothar Göttsche
Seconded: Walter Neumann, Jim Bryan
Enrique Artal Bartolo
Departamento de Matemáticas, IUMA, Facultad de Ciencias
Universidad de Zaragoza
c/ Pedro Cerbuna 12
E-50009 Zaragoza
José Ignacio Cogolludo-Agustín
Departamento de Matemáticas, IUMA, Facultad de Ciencias
Universidad de Zaragoza
c/ Pedro Cerbuna 12
E-50009 Zaragoza
Daniel Matei
Institute of Mathematics of the Romanian Academy
P.O. Box 1-764
014700 Bucharest