Chern numbers on positive vector bundles and combinatorics

Abstract

Combinatorial ideas are developed in this article to study Chern numbers on ample and numerically effective vector bundles. An effective lower bound for Chern numbers of ample vector bundles is established, which makes some progress towards a long-standing question. Along this line we prove that Chern numbers on nef vector bundles obey reverse dominance ordering, which improves upon some classical and recent results. We propose a simultaneous positivity question on (signed) Chern numbers of compact complex or Kähler manifolds whose (co)tangent bundles are semipositive in various senses, and show that it holds true for compact homogeneous complex manifolds.

18 pages

References in corpus (6)

• A survey on the Campana-Peternell Conjecture
• Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles
• Nonnegative Hermitian vector bundles and Chern numbers
• On characteristic forms of positive vector bundles, mixed discriminants and pushforward identities
• A note on Griffiths' conjecture about the positivity of Chern-Weil forms
• Characteristic numbers, Jiang subgroup and non-positive curvature