Geodesic
Finite Galois covers, cohomology jump loci, formality properties, and multinets
Dimca, Alexandru1  ; Papadima, Stefan2
1 Laboratoire J. A. Dieudonné, UMR du CNRS 6621, Université de Nice Sophia-Antipolis Parc Valrose, 06108 Nice Cedex 02, France
2 institute of Mathematics Simion Stoilow, P.O. Box 1-764, RO-014700 Bucharest, Romania
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 253-268

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We explore the relation between cohomology jump loci in a finite Galois cover, formality properties and algebraic monodromy action. We show that the jump loci of the base and total space are essentially the same, provided the base space is 1-formal and the monodromy action in degree 1 is trivial. We use reduced multinet structures on line arrangements to construct components of the first characteristic variety of the Milnor fiber in degree 1, and to prove that the monodromy action is non-trivial in degree 1. For an arbitrary line arrangement, we prove that the triviality of the monodromy in degree 1 can be detected in a precise way, by resonance varieties.

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Classification : 32S22, 52C30, 55N25, 55P62

Dimca, Alexandru 1 ; Papadima, Stefan 2

1 Laboratoire J. A. Dieudonné, UMR du CNRS 6621, Université de Nice Sophia-Antipolis Parc Valrose, 06108 Nice Cedex 02, France
2 institute of Mathematics Simion Stoilow, P.O. Box 1-764, RO-014700 Bucharest, Romania 
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     title = {Finite {Galois} covers, cohomology jump loci, formality properties, and multinets},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Dimca, Alexandru; Papadima, Stefan. Finite Galois covers, cohomology jump loci, formality properties, and multinets. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 2, pp. 253-268. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_2_253_0/