Framed sheaves on projective space and Quot schemes

Abstract

We prove that, given integers $m\ge 3$, $r\ge 1$ and $n\ge 0$, the moduli space of torsion free sheaves on ${\mathbb{P}}^m$ with Chern character $(r,0,\dots ,0,-n)$ that are trivial along a hyperplane $D\subset {\mathbb{P}}^m$ is isomorphic to the Quot scheme ${\mathrm{Quot}}_{{\mathbb{A}}^m}({\mathcal{O}}^{\oplus r},n)$ of $0$-dimensional length $n$ quotients of the free sheaf ${\mathcal{O}}^{\oplus r}$ on ${\mathbb{A}}^m$.

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