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Symplectic resolutions of quiver varieties

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arxiv 1602.00164 v6 pith:BO644DG6 submitted 2016-01-30 math.AG math.RT

Gwyn Bellamy , Travis Schedler This is my paper · ORCID
classification math.AGmath.RT
keywords symplecticquiverresolutionsvarietieslocusadmitalgebraicappear
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abstract

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 $\theta$-polystable points, generalizing a result of Le Bruyn; we study their \'etale 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.

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  1. A new addition to the zoo of isolated symplectic singularities

    math.AG 2025-05 conditional novelty 7.0 of 10

    A new 4-dimensional isolated locally simply-connected symplectic singularity is constructed, with non-reduced projective tangent cone, together with all 12 of its Q-factorial terminalisations.

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