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Communication Dans Un Congrès Année : 2014

Rationally connected manifolds and semipositivity of the Ricci curvature

Frédéric Campana
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  • PersonId : 931065
Jean-Pierre Demailly
Thomas Peternell
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  • PersonId : 931020

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.
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Dates et versions

hal-00739178 , version 1 (07-10-2012)
hal-00739178 , version 2 (21-01-2014)
hal-00739178 , version 3 (04-02-2018)

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Frédéric Campana, Jean-Pierre Demailly, Thomas Peternell. Rationally connected manifolds and semipositivity of the Ricci curvature. Conference in honor of Rob Lazarsfeld's 60th birthday, 2013, Ann harbor, United States. pp.71-91. ⟨hal-00739178v2⟩
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