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Hodge metrics and positivity of direct images

Christophe Mourougane·Shigeharu Takayama
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Abstract

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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Christophe Mourougane, Shigeharu Takayama. 2005-05-16. Hodge metrics and positivity of direct images. https://doi.org/10.1515/crelle.2007.039

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