Hilbert schemes for crepant partial resolutions

Alastair Craw; Ruth Wye

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arXiv · 2409.07408

Hilbert schemes for crepant partial resolutions

Alastair Craw·Ruth Wye

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Abstract

For $n\geq 1$, we construct the underlying reduced subscheme of 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. As a corollary, we compute the nef and movable cones of the Hilbert scheme of $n$ points on any crepant partial resolution of a Kleinian singularity.

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BibTeX RIS

Alastair Craw, Ruth Wye. 2024-09-11. Hilbert schemes for crepant partial resolutions. https://arxiv.org/abs/2409.07408

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