Smooth toric <i>G</i>-Hilbert schemes via <i>G</i>-graphs

Magda Sebestean

doi:10.1016/j.crma.2006.11.033

Algebraic Geometry

Smooth toric G-Hilbert schemes via G-graphs

Presented by: Jean-Pierre Demailly

Magda Sebestean ¹

¹ Institut de mathématiques de Jussieu, Université Paris 7 “Denis-Diderot”, 2, place Jussieu, 75251 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 344 (2007) no. 2, pp. 115-119.

Abstract
Résumé

We provide here an infinite family of finite subgroups ${G_{n} \subset {SL}_{n} (C)}_{n ⩾ 2}$ for which the G-Hilbert scheme $G_{n} - Hilb A^{n}$ is a crepant resolution of $A^{n} / G_{n}$ , via the Hilbert–Chow morphism. The proof is based on an explicit description of the toric structure of $G_{n} - Hilb A^{n}$ in terms of Nakamura's $G_{n}$ -graphs.

Nous décrivons ici une famille infinie de sous-groupes finis ${G_{n} \subset {SL}_{n} (C)}_{n ⩾ 2}$ , telle que le $G_{n}$ -schéma de Hilbert sur l'espace affine $A^{n}$ soit lisse et donne une résolution crépante de $A^{n} / G_{n}$ , pour tout $n ⩾ 2$ , via le morphisme de Hilbert–Chow. La preuve est basée sur une description explicite de la structure torique de $G_{n} - Hilb A^{n}$ , $n ⩾ 2$ , à l'aide de $G_{n}$ -graphes.

Received: 2006-03-27
Accepted: 2006-11-14
Published online: 2006-12-28

DOI: 10.1016/j.crma.2006.11.033

Author's affiliations:

Magda Sebestean ¹

¹ Institut de mathématiques de Jussieu, Université Paris 7 “Denis-Diderot”, 2, place Jussieu, 75251 Paris cedex 05, France

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     author = {Magda Sebestean},
     title = {Smooth toric {\protect\emph{G}-Hilbert} schemes via {\protect\emph{G}-graphs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {115--119},
     publisher = {Elsevier},
     volume = {344},
     number = {2},
     year = {2007},
     doi = {10.1016/j.crma.2006.11.033},
     language = {en},
}

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Magda Sebestean. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.11.033/

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