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Représentations linéaires des groupes kählériens : factorisations et conjecture de Shafarevich linéaire

Part of: Birational geometry (Co)homology theory Complex manifolds Families, fibrations

Published online by Cambridge University Press:  26 November 2014

Fréderic Campana ,
Benoît Claudon  and
Philippe Eyssidieux
Fréderic Campana
Affiliation:
Université de Lorraine, Institut Élie Cartan Nancy, UMR 7502, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France email Frederic.Campana@univ-lorraine.fr
Benoît Claudon
Affiliation:
Université de Lorraine, Institut Élie Cartan Nancy, UMR 7502, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France email Benoit.Claudon@univ-lorraine.fr
Philippe Eyssidieux
Affiliation:
Institut Fourier, Université Grenoble 1, 38402 Saint-Martin d’Hères Cedex, France email Philippe.Eyssidieux@ujf-grenoble.fr
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Abstract

We extend to compact Kähler manifolds some classical results on linear representation of fundamental groups of complex projective manifolds. Our approach, based on an interversion lemma for fibrations with tori versus general type manifolds as fibers, gives a refinement of the classical work of Zuo. We extend to the Kähler case some general results on holomorphic convexity of coverings such as the linear Shafarevich conjecture.

Résumé

Nous étendons aux variétés kählériennes compactes quelques résultats classiques sur les représentations linéaires des groupes fondamentaux des variétés projectives lisses. Notre approche, basée sur une interversion de fibrations à fibres tores vs variétés de type général, fournit une alternative à celle de [K. Zuo, Kodaira dimension and Chern hyperbolicity of the Shafarevich maps for representations of${\it\pi}_{1}$of compact Kähler manifolds, J. Reine Angew. Math. 472 (1996), 139–156]. Enfin nous étendons au cas kählérien les résultats généraux de convexité holomorphe pour les revêtements associés connus dans le cas projectif.

Keywords

Kähler manifoldsKähler groupsShafarevich morphismsholomorphic convexity

MSC classification

Primary: 32Q15: Kähler manifolds 14F35: Homotopy theory; fundamental groups 32Q30: Uniformization 14E20: Coverings 14D07: Variation of Hodge structures

Information

Type
Research Article
Information
Compositio Mathematica , Volume 151 , Issue 2 , February 2015 , pp. 351 - 376
Copyright
© The Author(s) 2014 

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