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Advances in Geometry

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Volume 18, Issue 4

Issues

Commuting matrices and the Hilbert scheme of points on affine spaces

Abdelmoubine A. Henni
  • Universidade Federal de Santa Catarina, Departamento de Matemática, Campus Universitário Trindade, CEP 88.040-900 Florianápolis-SC, Brasil
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/ Marcos Jardim
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  • IMECC - UNICAMP, Departamento de Matemática, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária, 13083-859 Campinas–SP, Brazil
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Published Online: 2018-07-20 | DOI: https://doi.org/10.1515/advgeom-2018-0011

Abstract

We give linear algebraic and 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 ℂ3 is irreducible for c ≤ 10.

Keywords: Hilbert scheme of points; monads

MSC 2010: 14C05

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About the article


Received: 2015-09-24

Revised: 2016-08-13

Published Online: 2018-07-20

Published in Print: 2018-10-25


Funding: AAH was supported by the FAPESP post-doctoral grant number 2009/12576-9. MJ is partially supported by the CNPq grant number 303332/2014-0 and the FAPESP grant number 2014/14743-8.


Citation Information: Advances in Geometry, Volume 18, Issue 4, Pages 467–482, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2018-0011.

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