Curvature of vector bundles associated to holomorphic fibrations

By B. Berndtsson. 2005

374 citations recorded by the source corpus.

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 nonsingular we prove that the hermitian vector bundle E over Y whose fibers over points y are the spaces of global sections over Xy to L ⊗ Kx/y, endowed with the L2-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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/a78f787cef6cfcc914dc943909e42325088158d2

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

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