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Characteristic varieties
of quasi-projective manifolds and orbifolds
Enrique Artal Bartolo, José Ignacio Cogolludo-Agustín and Daniel Matei |
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Geometry & Topology 17 (2013) 273–309
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Abstract |
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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. |
Keywords
characteristic varieties, local systems, cohomology jumping
loci, cohomology with twisted coefficients,
quasi-projective groups, orbicurves, orbifolds
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Mathematical Subject Classification 2010
Primary: 32S20, 32S50, 58K65
Secondary: 14B05, 14H30, 14H50
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References |
Publication
Received: 3 May 2012
Accepted: 22 September 2012
Published: 7 March 2013
Proposed: Lothar Göttsche
Seconded: Walter Neumann, Jim Bryan
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Authors |
| Enrique Artal Bartolo | |
| Departamento de Matemáticas, IUMA,
Facultad de Ciencias Universidad de Zaragoza c/ Pedro Cerbuna 12 E-50009 Zaragoza Spain |
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| http://riemann.unizar.es/geotop/WebGeoTo/Profes/eartal/ | |
| José Ignacio Cogolludo-Agustín | |
| Departamento de Matemáticas, IUMA,
Facultad de Ciencias Universidad de Zaragoza c/ Pedro Cerbuna 12 E-50009 Zaragoza Spain |
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| http://riemann.unizar.es/~jicogo/ | |
| Daniel Matei | |
| Institute of Mathematics of the
Romanian Academy P.O. Box 1-764 014700 Bucharest Romania |
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| http://www.imar.ro/~dmatei | |
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