arXiv subjects

Ruth Wye

Publications and source records attributed to Ruth Wye.

2 recordsLinked to original sources

arXiv2025

Stacky Resolutions of Kleinian Singularities and Nakajima Quiver Varieties

We construct a class of noncommutative crepant resolutions of any Kleinian singularity as noncommutative sheaves of algebras over its crepant partial resolutions. We argue that such resolutions are Morita equivalent to the canonical orbifold resolutions of the partial resolutions. Further, we study Hilbert schemes of points on both the crepant partial and noncommutative resolutions and show that they are Nakajima quiver varieties. Finally, we describe the nef and movable cones of these Hilbert schemes of points using tautological bundles on the crepant partial resolutions.

math.AG↗

arXiv2024

Hilbert schemes for crepant partial resolutions

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.

math.AG↗