Curvature of vector bundles and subharmonicity of Bergman kernels

الأصل · EN

In a previous paper, Berndtsson, we have studied a property of subharmonic dependence on a parameter of Bergman kernels for a family of weighted L²-spaces of holomorphic functions. Here we prove a result on the curvature of a vector bundle defined by this family of L²-spaces itself, which has the earlier results on Bergman kernels as a corollary. Applying the same arguments to spaces of holomorphic sections to line bundles over a locally trivial fibration we also prove that if a holomorphic vector bundle, V, over a complex manifold is ample in the sense of Hartshorne, then V V has an Hermitian metric with curvature strictly positive in the sense of Nakano.