Hilbert schemes for crepant partial resolutions
Algebraic Geometry
2025-06-02 v2 Representation Theory
Abstract
For , we construct the Hilbert scheme of 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.
Cite
@article{arxiv.2409.07408,
title = {Hilbert schemes for crepant partial resolutions},
author = {Alastair Craw and Ruth Wye},
journal= {arXiv preprint arXiv:2409.07408},
year = {2025}
}
Comments
v2: 15 pages, 1 figure, streamlined so that we now present only one proof of the main result. Second author's name updated