A note on the ADHM description of Quot schemes of points on affine\n spaces

2017/12/12 by Abdelmoubine Amar Henni, Henni, Abdelmoubine Amar, Douglas Magno Guimarães +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1712.04369

openalex publication_date 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an ADHM description of the Quot scheme of points rm\nQuot_\ℂⁿ(c,r), of length c and rank r on affine spaces\n\ℂⁿ which naturally extends both Baranovsky's representation of\nthe punctual Quot scheme on a smooth surface and the Hilbert scheme of points\non affine spaces \ℂⁿ, described by the first author and M. Jardim.\nUsing results on the variety of commuting matrices, and combining them with our\nconstruction, we prove new properties concerning irreducibility and reducedness\nof rm Quot_\ℂⁿ(c,r) and its punctual version rm\nQuot_ mathbbY^[p](c,r), where p is a fixed point on a smooth affine\nvariety mathbbY. In this last case we also study a connectedness result,\nfor some special cases of higher r and c.\n

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