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Article Dans Une Revue Journal für die reine und angewandte Mathematik Année : 2007

Hodge metrics and positivity of direct images

Résumé

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle $E$ on a complex manifold, and every positive integer $k$, the vector bundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.
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Dates et versions

hal-00004912 , version 1 (16-05-2005)
hal-00004912 , version 2 (19-11-2005)

Identifiants

Citer

Christophe Mourougane, Shigeharu Takayama. Hodge metrics and positivity of direct images. Journal für die reine und angewandte Mathematik, 2007, 2007 (606), pp.167-178. ⟨10.1515/CRELLE.2007.039⟩. ⟨hal-00004912v2⟩
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