Curvature of vector bundles associated to holomorphic fibrations

Bo Berndtsson

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Curvature of vector bundles associated to holomorphic fibrations

Bo Berndtsson

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Abstract

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$ are the spaces of global sections over $X_y$ to $L\gr K_{X/Y}$ endowed with the $L^2$-metric is (semi)-positive in the sense of Nakano. We also discuss various applications, among them a partial result on a conjecture of Griffiths on the positivity of ample bundles. This is a revised and much expanded version of a previous preprint with the title `` Bergman kernels and the curvature of vector bundles''.

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BibTeX RIS

Bo Berndtsson. 2005-11-09. Curvature of vector bundles associated to holomorphic fibrations. https://arxiv.org/abs/math/0511225

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