Nonnegative Hermitian vector bundles and Chern numbers

Abstract

We show in this article that if a holomorphic vector bundle has a nonnegative Hermitian metric in the sense of Bott and Chern, which always exists on globally generated holomorphic vector bundles, then some special linear combinations of Chern forms are strongly nonnegative. This particularly implies that all the Chern numbers of such a holomorphic vector bundle are nonnegative and can be bounded below and above respectively by two special Chern numbers. As applications, we obtain a family of new results on compact connected complex manifolds which are homogeneous or can be holomorphically immersed into complex tori, some of which improve several classical results.

18 pages, final version to appear in Mathematische Annalen

Cited by in corpus (4)

• On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
• A note on Griffiths' conjecture about the positivity of Chern-Weil forms
• Chern numbers on positive vector bundles and combinatorics
• Positivity of Schur forms for strongly decomposably positive vector bundles