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 \((r,0,\ldots ,0,-n)\) that are trivial along a hyperplane \(D \subset {\mathbb {P}}^m\) is isomorphic to the Quot scheme \(\mathrm{Quot}_{{\mathbb {A}}^m}({\mathscr {O}}^{\oplus r},n)\) of 0-dimensional length n quotients of the free sheaf \({\mathscr {O}}^{\oplus r}\) on \({\mathbb {A}}^m\). The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.

中文翻译：

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投影空间和报价方案上的框架滑轮

我们证明，给定整数\(m\ge 3\)、\(r\ge 1\)和\(n\ge 0\)，\({\mathbb {P}} ^m\)与陈字符\((r,0,\ldots ,0,-n)\)沿超平面\(D \subset {\mathbb {P}}^m\)同构于0 维长度n 个自由商的报价方案\(\mathrm{Quot}_{{\mathbb {A}}^m}({\mathscr {O}}^{\oplus r},n)\)捆\({\mathscr {O}}^{\oplus r}\)在\({\mathbb {A}}^m\) 上。通过比较这些模空间上的两种切线阻塞理论来证明。