The symplectic-singularity conjecture for multiplicative quiver varieties

Let Mq,θ(Q,α)\mathcal{M}_{q,\theta}(Q,\alpha) denote a multiplicative quiver variety. A symplectic singularity is a normal singular variety whose smooth locus carries a symplectic form extending to a regular two-form on every resolution. Symplectic-singularity conjecture. Every multiplicative quiver variety is a symplectic singularity. This would place multiplicative quiver varieties within the general framework of symplectic singularities and support the expected analysis of their symplectic resolutions; the statement remains open in the source.

Sources & referencesView supporting material

Primary source

Travis Schedler and Andrea Tirelli, “Symplectic resolutions for multiplicative quiver varieties and character varieties for punctured surfaces”, arXiv:1812.07687 (2019).

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