Deformations of the tangent bundle of projective manifolds

TL;DR

This paper studies when the tangent bundle of a projective manifold can be deformed, proposing a new conjecture that characterizes complex projective space based on these deformations.

Contribution

It introduces a new conjecture linking tangent bundle deformations to the characterization of complex projective space.

Findings

Conditions for non-trivial tangent bundle deformations identified

Conjectural criterion for complex projective space proposed

Insights into the structure of projective manifolds gained

Abstract

We investigate when the tangent bundle of a projective manifold has a non-trivial first order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.