HAL : hal-00739178, version 1

arXiv : 1210.2092

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Rationally connected manifolds and semipositivity of the Ricci curvature

Frédéric Campana 1, Jean-Pierre Demailly 2, Thomas Peternell 3

(01/10/2012)

This work establishes a structure theorem for compact Kähler manifolds with semipositive anticanonical bundle. Up to finite étale cover, it is proved that such manifolds split holomorphically and isometrically as a product of Ricci flat varieties and of rationally connected manifolds. The proof is based on a characterization of rationally connected manifolds through the non existence of certain twisted contravariant tensor products of the tangent bundle, along with a generalized holonomy principle for pseudoeffective line bundles. A crucial ingredient for this is the characterization of uniruledness by the property that the anticanonical bundle is not pseudoeffective.

1 :	Institut Elie Cartan Nancy (IECN)
	CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
2 :	Institut Fourier (IF)
	CNRS : UMR5582 – Université Joseph Fourier - Grenoble I
3 :	Mathematiches Institut Bayreuth
	Universitat Bayreuth

Équipe de recherche : Analyse et Géométrie Complexes

Domaine

:

Mathématiques/Géométrie algébrique

Mots Clés : Compact Kähler manifold – anticanonical bundle – Ricci curvature – uniruled variety – rationally connected variety – Bochner formula – holonomy principle – fundamental group – Albanese mapping – pseudoeffective line bundle – De Rham splitting

hal-00739178, version 1

http://hal.archives-ouvertes.fr/hal-00739178

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Contributeur : Jean-Pierre Demailly <>

Soumis le : Dimanche 7 Octobre 2012, 18:43:00

Dernière modification le : Lundi 8 Octobre 2012, 13:09:30