Nakano positivity and the L2-metric on the direct image of an adjoint positive line bundle

Details Nakano positivity and the L2-metric on the direct image of an adjoint positive line bundle Nakano positivity and the L2-metric on the direct image of an adjoint positive line bundle

1999-10-28

arxiv.org/abs/math/9910157v2

Mathematics

Complex Variables

11 pages, Latex. Some remarks suggested by J.P. Demailly are added. To appear in the Duke Mathematical Journal

Scientific paper

We prove that the $L^2$ metric on the direct image of an adjoint positive line bundle by a locally trivial submersion between projective manifolds is Nakano positive, under the assumption that the typical fiber has zero first Betti number. As a consequence, we get that the symmetric powers of an ample vector bundle tensorized by its determinant are Nakano positive, in particular Griffiths positive. This in turn gives vanishing theorems and an analytic characterization of ample vector bundles.

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