Recent Examples of Elementary Components of Hilbert Schemes of Points
Andrew Staal (University of the Fraser Valley)
Abstract: I will present some recent progress in the study of Hilbert schemes $\operatorname{Hilb}^d(\mathbb{A}^n)$ of $d$ points in affine space. Specifically, I will describe some recent examples of elementary components of Hilbert schemes of points. One infinite family of these answers a question posed by Iarrobino in the 80's: does there exist an irreducible component of the (local) punctual Hilbert scheme $\operatorname{Hilb}^d(\mathscr{O}_{\mathbb{A}^n,p})$ of dimension less than $(n-1)(d-1)$? A different family of elementary components arises from the Galois closure operation introduced by Bhargava--Satriano. In both situations, secondary families of elementary components also arise, providing further new examples of elementary components of Hilbert schemes of points.
This is joint work with Matt Satriano (U Waterloo).
algebraic geometrynumber theory
Audience: researchers in the discipline
Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).
We acknowledge the support of PIMS, NSERC, and SFU.
For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.
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| Organizer: | Katrina Honigs* |
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