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

TL;DR

This paper proves that Behrend's function varies on the Hilbert scheme of points in three-dimensional affine space for all n greater than or equal to 24.

Contribution

It establishes the non-constancy of Behrend's function on the Hilbert scheme for sufficiently large n, filling a gap in understanding its behavior.

Findings

Behrend's function is not constant on Hilb^n(A^3) for n  24

The proof applies to all n  24, confirming variability in the function

Advances knowledge of the geometric and enumerative properties of Hilbert schemes

Abstract

We prove the statement in the title for $n\geq 24$.