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Christophe Mourougane, Shigeharu Takayama

Hodge metrics and positivity of direct images

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 ⊗ 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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2007, 06/2007
Pages: 167 - 178

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