  Let C be an integral projective curve with planar singularities. Consider its
Jacobian J and the compactified Jacobian J'. We construct a flat family P of
Cohen-Macaulay sheaves on J' parametrized by J'; over J, the family P is the
Poincare line bundle. We prove that the Fourier-Mukai transform given by P is
an auto-equivalence of the derived category of J'.
