On the motive of the Hilbert scheme of points on a surface

2000/07/07 by Lothar Goettsche, Goettsche, Lothar · 5 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #math.AG

paper · pdf · doi:10.48550/arxiv.math/0007043

15 pages, Latex. The paper is the same as yesterdays revised version. Only these comments are corrected. The first version of the paper contained a wrong proof that the class of a motive in the Grothendieck group of motives determines its Chow groups with rational coefficients. The mistake was pointed out by B. Totaro. We include a proof also due to B. Totaro that the above statement follows from a conjecture of Beilinson and Murre

openalex publication_date 2000/07/07 · arxiv created 2000/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the class of the Hilbert scheme of points on a surface in the Grothendieck group of varieties. As a corollary we obtain its class in the Grothendieck group of motives. We give some applications to moduli spaces of sheaves on surfaces. The paper is related to math/0005249 of de Cataldo and Migliorini.

Cited by

• The \mathbbA¹-Euler characteristic of symmetric powers
• Involution on the Graded Grothendieck Ring of Varieties and \mathbbD-Singularities
• Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles
• Singularities of symmetric powers and irrationality of motivic zeta functions
• New components of Hilbert schemes of points and 2-step ideals

Related

• Hilbert schemes of points on surfaces
• The Chow groups and the motive of the Hilbert scheme of points on a surface
• Hilbert schemes of points on some classes of surface singularities
• Characteristic classes of the Hilbert schemes of points on non-compact simply-connected surfaces
• Generating series of classes of Hilbert schemes of points on orbifolds