Stability of Picard sheaves for vector bundles on curves

TL;DR

This paper proves the stability of Picard sheaves associated with stable vector bundles on curves with high slope, introducing a new homological method for testing their semistability.

Contribution

It establishes the stability of Picard sheaves for stable bundles with slope greater than 2g-1 and introduces a novel homological tool for semistability analysis.

Findings

Picard sheaves are stable for stable bundles with slope > 2g-1

Introduces a homological test for Picard sheaf semistability

Provides new insights into the geometry of vector bundles on curves

Abstract

We show that for any stable sheaf $E$ of slope $> 2g-1$ on a smooth, projective curve of genus $g$, the associated Picard sheaf $\hat{E}$ on the Picard variety of the curve is stable. We introduce a homological tool for testing semistability of Picard sheaves.