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

Indranil Biswas; Christophe Mourougane

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arXiv · math/9910157

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

Indranil Biswas·Christophe Mourougane

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Abstract

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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BibTeX RIS

Indranil Biswas, Christophe Mourougane. 2000-04-10. Nakano positivity and the L2-metric on the direct image of an adjoint positive line bundle. https://arxiv.org/abs/math/9910157

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