Segre forms and Kobayashi-L\"ubke inequality

TL;DR

This paper derives a pointwise Kobayashi-L"ubke inequality by analyzing Segre forms as direct images of powers of the first Chern form on projectivized bundles of holomorphic hermitian vector bundles.

Contribution

It introduces a novel approach to the Kobayashi-L"ubke inequality using Segre forms and their geometric interpretation as direct images.

Findings

Derived a pointwise Kobayashi-L"ubke inequality

Connected Segre forms with direct image formulas

Provided a new geometric perspective on curvature inequalities

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-L\"ubke inequality.