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Remarks on the holomorphic convexity of the universal covering space of a projective manifold.
Hodge metrics and the curvature of higher direct images
Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct image 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.
Some boundedness results for Fano-like Moishezon manifolds.
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