A compactification of the universal Picard variety

For any integer d, there is a universal Picard variety P_(d,g) over the moduli space of smooth curves of genus g, parametrizing isomorphism classes of line bundles of degree d on curves. P_(d,g) is quasiprojective. I'll talk about a compactification of it that lies over the moduli space of stable curves, and whose fibers over non-smooth curves parametrize equivalence classes of so-called quasistable curves with line bundles on them satisfying some combinatorial conditions.