Hilbert schemes for crepant partial resolutions

2024/09/11 by Alastair Craw, Ruth Wye, Craw, Alastair +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.2409.07408

openalex publication_date 2024/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

For n≥ 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.

Citations

• Algebraic Families on an Algebraic Surface

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