Symplectic resolutions of quiver varieties

• Gwyn Bellamy ^[1] ; Travis Schedler ^[2]
  1. [1] University of Glasgow

     University of Glasgow

     Reino Unido

     
  2. [2] Imperial College London

     Imperial College London

     Reino Unido

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 3, 2021
• Idioma: inglés
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• Resumen

  • In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically θ-polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT.