## Projective rational smoothness of varieties of representations for quivers of type $A$

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## Abstract:

Let ${\mathbf U}^+$ be the positive part of the quantized enveloping algebra ${\mathbf U}$ of type $A_n$. The change of basis between canonical, and PBW-basis of ${\mathbf U}^+$ 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 $A_n$. In this paper we study the local rational smoothness of these orbit closures and, in particular, the rational smoothness of their projectivization.## References

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*Rational smoothness of varieties of representations for quivers of type $A$*, preprint.

## Additional Information

**Ralf Schiffler**- Affiliation: Département de mathématiques, Université du Québec à Montréal, case postale 8888, succursale Centre-Ville, Montréal (Québec), H3C 3P8 Canada
- MR Author ID: 724459
- Email: ralf@math.uqam.ca
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2017067