Geodesic
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.

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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.

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.

Publié le :
DOI : 10.24033/asens.2242
Classification : 14F05, 14F45, 55N25.
Keywords: Local system, cohomology jump loci, smooth quasi-projective variety.
Mots-clés : Systémes locaux, lieux de saut de cohomologie, variété quasi-projective lisse. 
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     title = {Cohomology jump loci  of quasi-projective varieties},
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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://geodesic.mathdoc.fr/articles/10.24033/asens.2242/

Arapura, D. Higgs line bundles, Green-Lazarsfeld sets, and maps of Kähler manifolds to curves, Bull. Amer. Math. Soc., Volume 26 (1992), pp. 310-314 (ISSN: 0273-0979) | MR | Zbl | DOI

Arapura, D. Geometry of cohomology support loci for local systems. I, J. Algebraic Geom., Volume 6 (1997), pp. 563-597 (ISSN: 1056-3911) | MR | Zbl

Budur, N. Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers, Adv. Math., Volume 221 (2009), pp. 217-250 (ISSN: 0001-8708) | MR | Zbl | DOI

Deligne, P., Lecture Notes in Math., 163, Springer, 1970, 133 pages | MR | Zbl

Dimca, A., Universitext, Springer, 1992, 263 pages (ISBN: 0-387-97709-0) | MR | Zbl | DOI

Dimca, A.; Papadima, Ş. Non-abelian cohomology jump loci from an analytic viewpoint, Comm. Contemp. Math., Volume 16 (2014) (ISSN: 0219-1997) | MR | Zbl | DOI

Green, M.; Lazarsfeld, R. Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville, Invent. Math., Volume 90 (1987), pp. 389-407 (ISSN: 0020-9910) | MR | Zbl | DOI

Green, M.; Lazarsfeld, R. Higher obstructions to deforming cohomology groups of line bundles, J. Amer. Math. Soc., Volume 4 (1991), pp. 87-103 (ISSN: 0894-0347) | MR | Zbl | DOI

Mochizuki, T. Kobayashi-Hitchin correspondence for tame harmonic bundles. II, Geom. Topol., Volume 13 (2009), pp. 359-455 (ISSN: 1465-3060) | MR | Zbl | DOI

Nitsure, N. Moduli of semistable logarithmic connections, J. Amer. Math. Soc., Volume 6 (1993), pp. 597-609 (ISSN: 0894-0347) | MR | Zbl | DOI

Pink, R.; Roessler, D. A conjecture of Beauville and Catanese revisited, Math. Ann., Volume 330 (2004), pp. 293-308 (ISSN: 0025-5831) | MR | Zbl | DOI

Schnell, C. Holonomic D-modules on Abelian varieties, Publ. Math. IHÉS (2014) ( doi://10.1007/s10240-014-0061-x ) | mathdoc-id | MR

Schnell, C. Torsion points on cohomology support loci: from D-modules to Simpson's theorem, Rec. Adv. Alg. Geom. (2015) | MR | Zbl

Simpson, C. T. Harmonic bundles on noncompact curves, J. Amer. Math. Soc., Volume 3 (1990), pp. 713-770 (ISSN: 0894-0347) | MR | Zbl | DOI

Simpson, C. T. Subspaces of moduli spaces of rank one local systems, Ann. Sci. École Norm. Sup., Volume 26 (1993), pp. 361-401 (ISSN: 0012-9593) | MR | Zbl | mathdoc-id | DOI

Simpson, C. T. Moduli of representations of the fundamental group of a smooth projective variety. I, Publ. Math. IHÉS, Volume 79 (1994), pp. 47-129 (ISSN: 0073-8301) | MR | Zbl | mathdoc-id | DOI

Simpson, C. T. Moduli of representations of the fundamental group of a smooth projective variety. II, Publ. Math. IHÉS, Volume 80 (1994), pp. 5-79 (ISSN: 0073-8301) | MR | Zbl | mathdoc-id | DOI

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