The Tutte polynomial and toric Nakajima quiver varieties

Tarig Abdelgadir, Anton Mellit, Fernando Rodriguez Villegas

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

For a quiver Q with underlying graph Γ, we take M an associated toric Nakajima quiver variety. In this article, we give a direct relation between a specialization of the Tutte polynomial of Γ, the Kac polynomial of Q and the Poincaré polynomial of M. We do this by giving a cell decomposition of M indexed by spanning trees of Γ 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.
OriginalspracheEnglisch
Seiten (von - bis)1323-1339
Seitenumfang17
FachzeitschriftProceedings of the Royal Society of Edinburgh Section A: Mathematics
Jahrgang152
Ausgabenummer5
Frühes Online-Datum27 Okt. 2021
DOIs
PublikationsstatusVeröffentlicht - Okt. 2022

ÖFOS 2012

  • 101001 Algebra
  • 101012 Kombinatorik
  • 101009 Geometrie

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