Autoduality for treelike curves with planar singularities

Let C be a treelike curve, that is, a reduced curve whose irreducible components meet transversally at disconnecting points ofC. AssumeC has planar singularities. In this note we prove an Autoduality Theorem for C. More precisely, in [6] a natural Abel map A: C → $bar J$ to a certain compactification $bar J$ of the generalized Jacobian of C has been constructed. In this note we prove that the pullback map $A^* :Pic^0 (bar J) to Pic^0 (C)$ is an isomorphism.