Hodge metrics and the curvature of higher direct images

Details Hodge metrics and the curvature of higher direct images Hodge metrics and the curvature of higher direct images

2007-07-24

arxiv.org/abs/0707.3551v2

Mathematics

Algebraic Geometry

Arguments are simplified. To appear in Ann. Sci. Ecole Norm. Sup

Scientific paper

Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct images bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

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