We study the Zariski closures of orbits of representations of quivers of type , ou . 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 , ou . 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.
Keywords: quantum groups, representations of quivers, singularities, canonical basis
Mot clés : groupes quantiques, representations de carquois, singularites, base canonique
@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}, 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://archive.numdam.org/articles/10.5802/aif.2019/} }
TY - JOUR AU - Caldero, Philippe AU - Schiffler, Ralf TI - Rational smoothness of varieties of representations for quivers of Dynkin type JO - Annales de l'Institut Fourier PY - 2004 SP - 295 EP - 315 VL - 54 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2019/ DO - 10.5802/aif.2019 LA - en ID - AIF_2004__54_2_295_0 ER -
%0 Journal Article %A Caldero, Philippe %A Schiffler, Ralf %T Rational smoothness of varieties of representations for quivers of Dynkin type %J Annales de l'Institut Fourier %D 2004 %P 295-315 %V 54 %N 2 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2019/ %R 10.5802/aif.2019 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2019/
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