On the motive of the Quot scheme of finite quotients of a locally free sheaf

Abstract

Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [QuotX(E,n)] in terms of the power structure on the Grothendieck ring of varieties. This extends a recent result of Bagnarol, Fantechi and Perroni for curves, and a result of Gusein-Zade, Luengo and Melle-Hernández for Hilbert schemes. We compute this generating function for curves and we express the relative motive [QuotAd(O⊕r)→SymAd] as a plethystic exponential.