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.


https://hal.archives-ouvertes.fr/hal-00739178
Contributor : Jean-Pierre Demailly <>
Submitted on : Tuesday, January 21, 2014 - 10:20:16 PM
Last modification on : Tuesday, July 28, 2015 - 1:23:27 PM

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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. 2012. <hal-00739178v2>

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