Cohomology jump loci of quasi-projective varieties
[Lieux de saut pour la cohomologie de variétés quasi-projectives]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 1, pp. 227-236.

Dans cet article, on montre que les lieux de saut dans l'espace de systèmes locaux de rang un sur une variété lisse quasi-projective sont des réunions finies de subtores translatées par des éléments de torsion. Pour cela, nous utilisons un résultat récent de Dimca-Papadima, certaines techniques introduites par Simpson, ainsi que des propriétés de l'espace de moduli pour les connexions logarithmiques construit par Nitsure et Simpson.

We prove that the cohomology jump loci in the space of rank one local systems over a smooth quasi-projective variety are finite unions of torsion translates of subtori. The main ingredients are a recent result of Dimca-Papadima, some techniques introduced by Simpson, together with properties of the moduli space of logarithmic connections constructed by Nitsure and Simpson.

Publié le :
DOI : 10.24033/asens.2242
Classification : 14F05, 14F45, 55N25.
Keywords: Local system, cohomology jump loci, smooth quasi-projective variety.
Mot clés : Systémes locaux, lieux de saut de cohomologie, variété quasi-projective lisse. 
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     title = {Cohomology jump loci  of quasi-projective varieties},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {227--236},
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Budur, Nero; Wang, Botong. Cohomology jump loci  of quasi-projective varieties. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 1, pp. 227-236. doi : 10.24033/asens.2242. http://www.numdam.org/articles/10.24033/asens.2242/

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