Discriminant of Tautological Bundles on Symmetric Products of Curves

TL;DR

This paper derives a formula for the discriminant of tautological bundles on symmetric powers of curves, showing that the Bogomolov inequality does not impose new stability restrictions beyond known destabilising subbundles.

Contribution

It provides an explicit discriminant formula for tautological bundles on symmetric products of curves, clarifying stability conditions.

Findings

Discriminant formula for tautological bundles derived

Bogomolov inequality does not impose new restrictions

Destabilising subbundles are already known

Abstract

We compute a formula for the discriminant of tautological bundles on symmetric powers of a complex smooth projective curve. It follows that the Bogomolov inequality does not give a new restriction to stability of these tautological bundles. It only rules out tautological bundles which are already known to have the structure sheaf as a destabilising subbundle.