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The Tutte polynomial and toric Nakajima quiver varieties
Published online by Cambridge University Press: 27 October 2021
Abstract
For a quiver 
$Q$ with underlying graph 
$\Gamma$, we take 
$ {\mathcal {M}}$ an associated toric Nakajima quiver variety. In this article, we give a direct relation between a specialization of the Tutte polynomial of 
$\Gamma$, the Kac polynomial of 
$Q$ and the Poincaré polynomial of 
$ {\mathcal {M}}$. We do this by giving a cell decomposition of 
$ {\mathcal {M}}$ indexed by spanning trees of 
$\Gamma$ and ‘geometrizing’ the deletion and contraction operators on graphs. These relations have been previously established in Hausel–Sturmfels [6] and Crawley-Boevey–Van den Bergh [3], however the methods here are more hands-on.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 5 , October 2022 , pp. 1323 - 1339
- Copyright
- Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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