Positivity vs. slope semistability for bundles with vanishing discriminant

TL;DR

This paper provides an algebraic proof, valid in any characteristic, establishing the equivalence between strongly slope semistable vector bundles with vanishing discriminant and vanishing determinant, and numerically flat bundles.

Contribution

It offers a characteristic-independent algebraic proof of a known equivalence in vector bundle theory and addresses a related open question.

Findings

Proved the equivalence algebraically in arbitrary characteristic.

Confirmed the relationship between slope semistability and numerical flatness.

Addressed a question posed by Misra.

Abstract

We give an algebraic proof valid in arbitrary characteristic for the known equivalence between (strongly) slope semistable vector bundles with vanishing discriminant and vanishing determinant and numerically flat bundles. We also address a related question of Misra.