Deciding Stability of Sheaves on Curves

TL;DR

This paper presents an algorithm to determine the semistability of kernel sheaves on smooth projective curves by leveraging symmetric powers to identify destabilizing subbundles.

Contribution

It introduces a novel algorithmic approach for checking semistability of sheaves on curves, utilizing symmetric powers to detect destabilizing subbundles.

Findings

Algorithm successfully determines semistability of kernel sheaves.

Uses symmetric powers to identify destabilizing subbundles.

Applicable over algebraically closed fields.

Abstract

We give an algorithm to determine whether a kernel sheaf over a smooth projective curve over an algebraically closed field is semistable. The algorithm uses symmetric powers to make destabilizing subbundles visible as global sections.