On the motive of the Hilbert scheme of points on a surface
Abstract
Description
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.
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
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