Rationally connected manifolds and semipositivity of the Ricci curvature

Abstract : 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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Communication dans un congrès
Hacon Christopher D. et al. Conference in honor of Rob Lazarsfeld's 60th birthday, 2013, Ann harbor, United States. Cambridge university Press, 417, pp.71-91, 2014, Lecture Note Series
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Dernière modification le : jeudi 11 janvier 2018 - 06:12:15
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  • HAL Id : hal-00739178, version 2
  • ARXIV : 1210.2092

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Frédéric Campana, Jean-Pierre Demailly, Thomas Peternell. Rationally connected manifolds and semipositivity of the Ricci curvature. Hacon Christopher D. et al. Conference in honor of Rob Lazarsfeld's 60th birthday, 2013, Ann harbor, United States. Cambridge university Press, 417, pp.71-91, 2014, Lecture Note Series. 〈hal-00739178v2〉

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