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

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.

arXiv comment15 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

References in corpus (4)

• On the Cobordism Class of the Hilbert Scheme of a Surface
• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
• Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces
• On blowup formulae for the S-duality conjecture of Vafa and Witten

Cited by in corpus (1)

• Motivic classes of Quot-schemes on surfaces