The Chow groups and the motive of the Hilbert scheme of points on a surface

TL;DR

This paper computes the Chow motive and Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface, advancing understanding of its algebraic and geometric structure.

Contribution

It provides explicit calculations of the Chow motive and Chow groups for the Hilbert scheme of points on a surface, a previously less understood area.

Findings

Chow motive of the Hilbert scheme is explicitly computed.

Chow groups with rational coefficients are determined.

Results enhance understanding of algebraic cycles on Hilbert schemes.

Abstract

We compute the Chow motive and the Chow groups with rational coefficients of the Hilbert scheme of points on a smooth algebraic surface