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arXiv · 1304.3028

Commuting matrices and the Hilbert scheme of points on affine spaces

Abdelmoubine Amar Henni·Marcos Jardim
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Abstract

We give a linear algebraic and a monadic descriptions of the Hilbert scheme of points on the affine space of dimension $n$ which naturally extends Nakajima's representation of the Hilbert scheme of points on the plane. As an application of our ideas and recent results from the literature on commuting matrices, we show that the Hilbert scheme of $c$ points on $(\C^3)$ is irreducible for $c\le 10$.

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Abdelmoubine Amar Henni, Marcos Jardim. 2013-04-10. Commuting matrices and the Hilbert scheme of points on affine spaces. https://doi.org/10.1515/advgeom-2018-0011

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