hal-00739178, version 1
Rationally connected manifolds and semipositivity of the Ricci curvature
Frédéric Campana
1Jean-Pierre Demailly
2Thomas Peternell 3
Résumé : 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
- 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
- Commentaire : 16 pages
- hal-00739178, version 1
- http://hal.archives-ouvertes.fr/hal-00739178
- oai:hal.archives-ouvertes.fr:hal-00739178
- Contributeur : Jean-Pierre Demailly
- Soumis le : Dimanche 7 Octobre 2012, 18:43:00
- Dernière modification le : Lundi 8 Octobre 2012, 13:09:30
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