We give an Atiyah–Drinfel’d–Hitchin–Manin (ADHM) description of the Quot scheme of points Quotℂn(c,r), of length c and rank r on affine spaces ℂn which naturally extends both Baranovsky’s representation of the punctual Quot scheme on a smooth surface and the Hilbert scheme of points on affine spaces ℂn, described by the first author and M. Jardim. Using results on the variety of commuting matrices, and combining them with our construction, we prove new properties concerning irreducibility and reducedness of Quotℂn(c,r) and its punctual version Quot𝕐[p](c,r), where p is a fixed point on a smooth affine variety 𝕐. In this last case, we also study a connectedness result, for some special cases of higher r and c.

中文翻译：

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关于仿射空间上点的引用方案的 ADHM 描述

我们给出了 Quot 点方案的 Atiyah-Drinfel'd-Hitchin-Manin (ADHM) 描述报价ℂn(C,r),长度C和排名r在仿射空间上ℂn它自然地扩展了 Baranovsky 在光滑表面上的准时 Quot 方案和仿射空间上点的 Hilbert 方案的表示ℂn,由第一作者和 M. Jardim 描述。使用各种交换矩阵的结果，并将它们与我们的构造相结合，我们证明了关于不可约性和约简性的新性质报价ℂn(C,r)及其准时版本报价𝕐[p](C,r),在哪里p是光滑仿射簇上的不动点𝕐. 在最后一种情况下，我们还研究了一个连通性结果，对于更高的一些特殊情况r和C.