Behrend's function is constant on Hilb^n(C^3)

TL;DR

This paper proves that Behrend's function remains constant on the Hilbert scheme of points in three-dimensional complex space, with implications for the structure and properties of these moduli spaces.

Contribution

It establishes the constancy of Behrend's function on Hilb^n(C^3) and relates motivic zeta functions to the Euler characteristic of Milnor fibers, extending to moduli schemes on resolutions of ADE singularities.

Findings

Behrend's function is constant on Hilb^n(C^3)

Milnor fibers have zero Euler characteristic

Hilb^n(C^3) is generically reduced

Abstract

We prove that Behrend's function is constant on Hilb^n(C^3). A calculation of motivic zeta functions shows the relevant Milnor fibers have zero Euler characteristic. As a corollary we see that Hilb^n(C^3) is generically reduced. These results extend to moduli schemes of points and curves on resolutions of ADE singularities C \times Y_G.