Rational smoothness of varieties of representations for quivers of Dynkin type

Philippe Caldero[1]; Ralf Schiffler

  • [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 (2004)

  • Volume: 54, Issue: 2, page 295-315
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Caldero, Philippe, and Schiffler, Ralf. "Rational smoothness of varieties of representations for quivers of Dynkin type." Annales de l’institut Fourier 54.2 (2004): 295-315. <http://eudml.org/doc/116112>.

@article{Caldero2004,
abstract = {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.},
affiliation = {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)},
author = {Caldero, Philippe, Schiffler, Ralf},
journal = {Annales de l’institut Fourier},
keywords = {quantum groups; representations of quivers; singularities; canonical basis},
language = {eng},
number = {2},
pages = {295-315},
publisher = {Association des Annales de l'Institut Fourier},
title = {Rational smoothness of varieties of representations for quivers of Dynkin type},
url = {http://eudml.org/doc/116112},
volume = {54},
year = {2004},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 2
SP - 295
EP - 315
AB - 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.
LA - eng
KW - quantum groups; representations of quivers; singularities; canonical basis
UR - http://eudml.org/doc/116112
ER -

References

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