Rational smoothness of varieties of representations for quivers of Dynkin type

Caldero, Philippe; Schiffler, Ralf

doi:10.5802/aif.2019

Rational smoothness of varieties of representations for quivers of Dynkin type
[Lissité rationnelle des variétés de représentations pour les carquois de type Dynkin]

Caldero, Philippe ¹ ; Schiffler, Ralf

¹ Université Claude Bernard Lyon I, Département de Mathématiques, 69622 Villeurbanne (France), Carleton University, School of mathematics and statistics, 1125 Colonel By drive, room 4302 Herzberg building, Ottawa, Ontario K1S 5B6 (Canada)

Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 295-315.

Résumé
Abstract

On étudie les clôtures au sens de Zariski des orbites de représentations des carquois de type $A$ , $D$ ou $E$ . A l’aide de la base canonique de Lusztig, on caractérise les clotures d’orbites rationnellement lisses et l’on prouve que ces variétés sont lisses si et seulement si elle sont rationnellement lisses.

We study the Zariski closures of orbits of representations of quivers of type $A$ , $D$ ou $E$ . With the help of Lusztig’s canonical base, we characterize the rationally smooth orbit closures and prove in particular that orbit closures are smooth if and only if they are rationally smooth.

Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2019

Classification : 17B37, 16G20, 14B05
Keywords: quantum groups, representations of quivers, singularities, canonical basis
Mot clés : groupes quantiques, representations de carquois, singularites, base canonique

Affiliations des auteurs :

Caldero, Philippe ¹ ; Schiffler, Ralf

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     author = {Caldero, Philippe and Schiffler, Ralf},
     title = {Rational smoothness of varieties of representations for quivers of {Dynkin} type},
     journal = {Annales de l'Institut Fourier},
     pages = {295--315},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     doi = {10.5802/aif.2019},
     zbl = {02123568},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.2019/}
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Caldero, Philippe; Schiffler, Ralf. Rational smoothness of varieties of representations for quivers of Dynkin type. Annales de l'Institut Fourier, Tome 54 (2004) no. 2, pp. 295-315. doi : 10.5802/aif.2019. http://www.numdam.org/articles/10.5802/aif.2019/

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