Motivic Hilbert zeta functions of curves are rational

TL;DR

This paper proves that the motivic Hilbert zeta function for reduced curves is a rational function, advancing understanding of the structure of Hilbert schemes in algebraic geometry.

Contribution

The paper establishes the rationality of the motivic Hilbert zeta function specifically for reduced curves, a new result in the study of Hilbert schemes.

Findings

Motivic Hilbert zeta function of reduced curves is rational.

Provides new insights into the structure of Hilbert schemes of points.

Advances algebraic geometry by linking motivic functions and curve properties.

Abstract

The motivic Hilbert zeta function of a variety is the generating function for classes in the Grothendieck ring of varieties of Hilbert schemes of points of the variety. In this paper, the motivic Hilbert zeta function of a reduced curve is shown to be rational.