  Let C be an integral projective curve with surficial singularities. We prove
that topologically trivial line bundles on the compactified Jacobian of C are
in one-to-one correspondence with line bundles on C (the autoduality
conjecture), and compute the cohomology of the line bundles. We also show that
the natural Fourier-Mukai functor between the derived categories of
quasi-coherent sheaves on the Jacobian and on the compactified Jacobian is
fully faithful.
