Exterior power of stable vector bundle destabilized by Frobenius pull-back

TL;DR

This paper demonstrates that in positive characteristic, there exist stable vector bundles on smooth projective curves whose exterior powers become destabilized, revealing new instability phenomena in algebraic geometry.

Contribution

It establishes the existence of stable vector bundles with non-semi-stable exterior powers under Frobenius pull-back on curves of genus at least 2.

Findings

Existence of stable bundles with destabilized exterior powers

Destabilization occurs under Frobenius pull-back in positive characteristic

Results apply to curves of genus g ≥ 2

Abstract

In this paper, we prove that for any smooth projective curve $C$ of genus $g\geq2$ over an algebraically closed field of positive characteristic, there exists a stable vector bundle over $C$ whose exterior power is not semi-stable.