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

Schiffler, Ralf

doi:10.1090/S1088-4165-03-00182-1

Projective rational smoothness of varieties of representations for quivers of type $A$
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by Ralf Schiffler

Represent. Theory 7 (2003), 549-586

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

Published electronically: November 18, 2003

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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.

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Rational smoothness of varieties of representations for quivers of type $A$

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