Hodge metrics and positivity of direct images

Details Hodge metrics and positivity of direct images Hodge metrics and positivity of direct images

2005-05-16

arxiv.org/abs/math/0505324v2

Mathematics

Algebraic Geometry

revised and expanded version of "A positivity property of ample vector bundles"

Scientific paper

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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