On compact K\"ahler manifold with strongly pseudo-effective tangent bundle

TL;DR

This paper investigates the properties of compact Kähler manifolds with strongly pseudo-effective tangent bundles, providing new proofs and characterizations related to big tangent bundles and nef vector bundles.

Contribution

It offers a new proof that projective spaces are the only projective manifolds with big tangent bundles and characterizes nef vector bundles in this context.

Findings

Only projective spaces have big tangent bundles among projective manifolds.

Provides a new proof regarding strongly pseudo-effective tangent bundles.

Characterizes nef vector bundles on compact Kähler manifolds.

Abstract

In the first part of this note, we discuss the compact K\"ahler manifold with a strongly pseudo-effective tangent bundle. In the second part, we give new proof of the fact that the only projective manifolds with the big tangent bundle are the projective spaces. In the third part, we give a characterisation of nef vector bundle.