English

Hilbert schemes for crepant partial resolutions

Algebraic Geometry 2025-06-02 v2 Representation Theory

Abstract

For n1n\geq 1, we construct the Hilbert scheme of nn 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.

Keywords

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

R2 v1 2026-06-28T18:41:28.387Z