# Strict and non strict positivity of direct image bundles - Mathematics > Algebraic Geometry

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Abstract: This paper is a sequel to \cite{Berndtsson}. In that paper we studied thevector bundle associated to the direct image of the relative canonical bundleof a smooth K\-ahler morphism, twisted with a semipositive line bundle. Weproved that the curvature of a such vector bundles is always semipositive inthe sense of Nakano. Here we adress the question if the curvature is strictlypositive when the Kodaira-Spencer class does not vanish. We prove that this isso provided the twisting line bundle is stricty positive along fibers, but notin general.

Autor: Bo Berndtsson

Fuente: https://arxiv.org/