Semistability of Certain Bundles on Second Symmetric Power of a Curve

TL;DR

This paper investigates the semistability of a rank 4 vector bundle on the second symmetric power of a curve, constructed from a stable rank 2 bundle on the original curve, contributing to the understanding of vector bundle stability in algebraic geometry.

Contribution

It establishes conditions under which the constructed bundle on the symmetric power is semistable, providing new insights into the stability properties of bundles on symmetric powers.

Findings

Semistability conditions for the bundle $_2(E)$ are derived.

The paper extends stability analysis from the original curve to its symmetric power.

Results contribute to the theory of vector bundles on symmetric products of curves.

Abstract

Let $C$ be a smooth irreducible projective curve and $E$ be a rank 2 stable vector bundle on $C$. Then one can associate a rank 4 vector bundle $\mathcal{F}_2(E)$ on $S^2(C)$, second symmetric power of $C$. Our goal in this article is to study semistability of this bundle.