Tangent, cotangent, normal and conormal bundles are almost never instanton bundles

TL;DR

This paper provides an elementary, characteristic-free proof that tangent, cotangent, normal, and conormal bundles are almost never instanton bundles, generalizing recent results for Ulrich bundles and discussing related twists.

Contribution

It introduces a new elementary proof for the non-instanton nature of certain bundles, extending previous results to a broader class of bundles and characteristic settings.

Findings

Tangent, cotangent, normal, and conormal bundles are almost never instanton bundles.

The proof is elementary and characteristic-free.

Results extend to twists of the cotangent bundle and suggest possible extensions for tangent bundles.

Abstract

In this very short note we give an elementary characteristic free proof of the result claimed in the title (see Theorem 1.2 for a more precise formulation), generalizing a recent result proved for Ulrich bundles over the complex field by V. Benedetti, P. Montero, Y. Prieto Monta\~nez, S. Troncoso. Moreover, we also give a similar result about the twists of the cotangent bundle and make some comments about the possibility to obtain an analogous result for twists of the tangent bundle.