Prym map and second Gaussian map for Prym-canonical line bundles

We show that the second fundamental form of the Prym map lifts the second Gaussian map μAμA of the Prym-canonical bundle. We prove, by degeneration to binary curves, that μAμA is surjective for the general point [C,A][C,A] of RgRg for g≥20g≥20.