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

Let X be a smooth variety, E a locally free sheaf on X. We express the generating function of the motives [Quot (X) (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-Hernandez for Hilbert schemes. We compute this generating function for curves and we express the relative motive [Quot(Ad)(partial derivative(circle times r)) -> Sym A(d)] as a plethystic exponential. (C) 2020 Elsevier Masson SAS. All rights reserved.