Segre forms and Kobayashi-Lübke inequality

Abstract

Starting from the description of Segre forms as direct images of (powers of) the first Chern form of the (anti)tautological line bundle on the projectivized bundle of a holomorphic hermitian vector bundle, we derive a version of the pointwise Kobayashi-Lübke inequality.

14 pages, no figures, comments are really very welcome! v2: Title changed, and added how to formally derive our main inequality from the Kobayashi-Lübke one following the suggestions of an anonymous referee. v3: some other minor changes and a remark added in the introduction following referee's suggestions. Final version, to appear on Math. Z