The moduli space of torsion-free sheaves with quasi-maximal third Chern class

In this paper, we investigate the geometry of the Gieseker moduli space of semistable rank $2$ torsion-free sheaves on $\mathbb{P}^3$ with Chern classes $(c_1, c_2, c_3) = (-1, c_2, c_2^2-2)$ for $c_2 \geq 2$. We use the modular Serre correspondence to relate these moduli spaces to spaces of pairs a