On the semistability of instanton sheaves over certain projective varieties

TL;DR

This paper proves semistability of certain instanton bundles and stability of specific linear bundles on projective varieties with cyclic Picard group, establishing sharp bounds for these properties.

Contribution

It establishes semistability and stability results for instanton and linear bundles on projective varieties, with precise bounds and sharpness analysis.

Findings

Instanton bundles of rank r ≤ 2n-1 are semistable.

Linear bundles of rank r ≤ n with nonzero first Chern class are stable.

Bounds for stability and semistability are shown to be sharp.

Abstract

We show that instanton bundles of rank $r\le 2n-1$, defined as the cohomology of certain linear monads, on an $n$-dimensional projective variety with cyclic Picard group are semistable in the sense of Mumford-Takemoto. Furthermore, we show that rank $r\le n$ linear bundles with nonzero first Chern class over such varieties are stable. We also show that these bounds are sharp.