Seshadri constants on some Quot schemes

Let E be a vector bundle of rank n on P-1. Fix a positive integer d. Let Q(E, d) denote the Quot scheme of torsion quotients of E of degree d and let Gr(E, d) denote the Grassmann bundle that parametrizes the d-dimensional quotients of the fibers of E. We compute Seshadri constants of ample line bundles on Q(E, d) and Gr(E, d).