Stability of Secant Bundles on Second Symmetric Power of Curves

TL;DR

This paper investigates the stability properties of secant bundles derived from stable bundles on curves, establishing a link between moduli spaces of bundles on curves and their symmetric powers.

Contribution

It introduces criteria for the stability of secant bundles on the second symmetric power of a curve and constructs an immersion between their moduli spaces.

Findings

Stability conditions for secant bundles are established.

An explicit immersion between moduli spaces is constructed.

Results connect bundle stability on curves to symmetric powers.

Abstract

Given a rank $r$ stable bundle over a smooth irreducible projective curve $C,$ there is an associated rank $2r$ bundle over $S^2(C),$ the second symmetric power of $C.$ In this article we study the stability of this bundle. As a consequence we get an immersion from the moduli space of stable bundles over $C$ to the associated moduli space of stable bundles over $S^2(C).$