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Hilbert schemes for crepant partial resolutions (2409.07408v2)
Published 11 Sep 2024 in math.AG and math.RT
Abstract: For $n\geq 1$, we construct the Hilbert scheme of $n$ points on any crepant partial resolution of a Kleinian singularity as a Nakajima quiver variety for an explicit GIT stability parameter. This generalises and unifies existing quiver variety constructions of the Hilbert scheme of points on the minimal resolution of a Kleinian singularity, and on the Kleinian singularity itself.
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