The Hilbert scheme of points on a threefold: Broken Gorenstein structures and linkage
Abstract
Abstract We investigate the Hilbert scheme of points on a smooth threefold. We introduce a notion of broken Gorenstein structure for finite schemes, and show that its existence guarantees smoothness on the Hilbert scheme. Moreover, we conjecture that it is exhaustive: every smooth point admits a broken Gorenstein structure. We give an explicit characterization of the smooth points on the Hilbert scheme of A 3 \mathbb{A}^{3} corresponding to monomial ideals. We investigate the nature of the singular points, and prove several conjectures by Hu. Along the way, we obtain a number of additional results, related to linkage classes, nested Hilbert schemes, and a bundle on the Hilbert scheme of a surface.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Mathematics and Applications
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Journal für die reine und angewandte Mathematik (Crelles Journal)
- Publisher
- Walter de Gruyter GmbH
- Volume
- 2026
- Issue
- 833
- Pages
- 67–109
- Publication date
- 2 March 2026
- Language
- EN