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

Biswas, Indranil; Mourougane, Christophe

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

Authors

Description

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