Rational smoothness of varieties of representations for quivers of Dynkin type
Annales de l'Institut Fourier, Volume 54 (2004) no. 2, p. 295-315
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.
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.
DOI : https://doi.org/10.5802/aif.2019
Classification:  17B37,  16G20,  14B05
Keywords: quantum groups, representations of quivers, singularities, canonical basis
@article{AIF_2004__54_2_295_0,
     author = {Caldero, Philippe and Schiffler, Ralf},
     title = {Rational smoothness of varieties of representations for quivers of Dynkin type},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {2},
     year = {2004},
     pages = {295-315},
     doi = {10.5802/aif.2019},
     zbl = {02123568},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2004__54_2_295_0}
}
Caldero, Philippe; Schiffler, Ralf. Rational smoothness of varieties of representations for quivers of Dynkin type. Annales de l'Institut Fourier, Volume 54 (2004) no. 2, pp. 295-315. doi : 10.5802/aif.2019. http://www.numdam.org/item/AIF_2004__54_2_295_0/

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