Torelli group action on the configuration space of a surface

We show that the Torelli group of a closed surface of genus [Formula: see text] acts nontrivially on the rational cohomology of the space of [Formula: see text]-element subsets of that surface. This implies that for a Riemann surface of genus [Formula: see text], the mixed Hodge structure on the space of its positive, reduced divisors of degree [Formula: see text] does in general not split over [Formula: see text].