Algebraic Geometry
Smooth toric G-Hilbert schemes via G-graphs
Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 115-119.

We provide here an infinite family of finite subgroups {GnSLn(C)}n2 for which the G-Hilbert scheme Gn-HilbAn is a crepant resolution of An/Gn, via the Hilbert–Chow morphism. The proof is based on an explicit description of the toric structure of Gn-HilbAn in terms of Nakamura's Gn-graphs.

Nous décrivons ici une famille infinie de sous-groupes finis {GnSLn(C)}n2, telle que le Gn-schéma de Hilbert sur l'espace affine An soit lisse et donne une résolution crépante de An/Gn, pour tout n2, via le morphisme de Hilbert–Chow. La preuve est basée sur une description explicite de la structure torique de Gn-HilbAn, n2, à l'aide de Gn-graphes.

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DOI: 10.1016/j.crma.2006.11.033
Sebestean, Magda 1

1 Institut de mathématiques de Jussieu, Université Paris 7 “Denis-Diderot”, 2, place Jussieu, 75251 Paris cedex 05, France
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Sebestean, Magda. Smooth toric G-Hilbert schemes via G-graphs. Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 115-119. doi : 10.1016/j.crma.2006.11.033. http://www.numdam.org/articles/10.1016/j.crma.2006.11.033/

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