Projective rational smoothness of varieties of representations for quivers of type

Author:
Ralf Schiffler

Journal:
Represent. Theory **7** (2003), 549-586

MSC (2000):
Primary 17B37; Secondary 32S60, 16G70

DOI:
https://doi.org/10.1090/S1088-4165-03-00182-1

Published electronically:
November 18, 2003

MathSciNet review:
2017067

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be the positive part of the quantized enveloping algebra of type . The change of basis between canonical, and PBW-basis of has a geometric interpretation in terms of local intersection cohomology of some affine algebraic varieties, namely the Zariski closures of orbits of representations of a quiver of type . In this paper we study the local rational smoothness of these orbit closures and, in particular, the rational smoothness of their projectivization.

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Additional Information

**Ralf Schiffler**

Affiliation:
Département de mathématiques, Université du Québec à Montréal, case postale 8888, succursale Centre-Ville, Montréal (Québec), H3C 3P8 Canada

Email:
ralf@math.uqam.ca

DOI:
https://doi.org/10.1090/S1088-4165-03-00182-1

Received by editor(s):
October 24, 2002

Received by editor(s) in revised form:
September 2, 2003

Published electronically:
November 18, 2003

Additional Notes:
The author was supported in part by FCAR Grant

Article copyright:
© Copyright 2003
American Mathematical Society