  We prove that certain degenerate abelian varieties, the compactified Jacobian
of a nodal curve and a stable quasiabelian variety, satisfy autoduality. We
establish this result by proving a comparison theorem that relates the
associated family of Picard schemes to the N\'eron model, a result of
independent interest. In our proof, a key fact is that the total space of a
suitable family of compactified Jacobians has rational singularities.
