Abstract:
Let $\mathcal I(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on $\mathbb P^3$. It is known that $\mathcal I(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since every rank $2$ instanton bundle on $\mathbb P^3$ is stable, we may regard $\mathcal I(n)$ as an open subset of the projective Gieseker–Maruyama moduli scheme $\mathcal M(n)$ of rank $2$ semistable torsion free sheaves $F$ on $\mathbb P^3$ with Chern classes $c_1=c_3=0$ and $c_2=n$, and consider the closure $\overline{\mathcal I(n)}$ of $\mathcal I(n)$ in $\mathcal M(n)$.
We construct some of the irreducible components of dimension $8n-4$ of the boundary $\partial\mathcal I(n):=\overline{\mathcal I(n)}\setminus\mathcal I(n)$. These components generically lie in the smooth locus of $\mathcal M(n)$ and consist of rank $2$ torsion free instanton sheaves with singularities along rational curves.
Key words and phrases:sheaves on projective spaces, instantons, moduli spaces of sheaves, stable sheaves.