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Mathematics, Algebraic Geometry
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.
