On the motive of the nested Quot scheme of points on a curve

Let C be a smooth curve over an algebraically closed field k, and let E be a locally free sheaf of rank r. We compute, for every d > 0, the generating function of the motives [QuotC(E, n)] is an element of K0(Vark), varying n = (0 < n1 < middot middot middot < nd), where QuotC(E,n) is the nested Quot scheme of points, parametrising 0-dimensional subsequent quotients E->> Td -middot middot middot->> T1 of fixed length ni = chi(Ti). The resulting series, obtained by exploiting the Bialynicki-Birula decomposition, factors into a product of shifted motivic zeta functions of C. In particular, it is a rational function.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).