Geometry & Topology Volume 29, issue 8 (2025)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Behrend's function is not constant on $\mathrm{Hilb}^n(\mathbb{A}^3)$

Joachim Jelisiejew, Martijn Kool and Reinier F Schmiermann

Geometry & Topology 29 (2025) 4469–4476

DOI: 10.2140/gt.2025.29.4469

Abstract

We prove that Behrend’s function is not constant on ${Hilb}^{n} (𝔸^{3})$ for $n \geq 24$ .

Keywords

Behrend function, Hilbert schemes on threefolds, critical loci

Mathematical Subject Classification

Primary: 14C05, 14N35

Secondary: 14L30

References

Publication

Received: 21 May 2024

Revised: 5 November 2024

Accepted: 20 February 2025

Published: 26 November 2025

Proposed: Jim Bryan

Seconded: Marc Levine, Mark Gross

Authors

Joachim Jelisiejew
Faculty of Mathematics, Informatics, and Mechanics University of Warsaw Warsaw Poland

Martijn Kool
Mathematical Institute Utrecht University Utrecht Netherlands

Reinier F Schmiermann
Mathematical Institute Utrecht University Utrecht Netherlands

© 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

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