Autoduality of compactified Jacobians for curves with plane singularities

Abstract

Let C C be an integral projective curve with at most planar singularities. Consider its Jacobian J J and the compactified Jacobian J ¯ \overline {J} . We construct a flat family P ¯ \overline {P} of Cohen-Macaulay sheaves on J ¯ \overline {J} parametrized by J ¯ \overline {J} ; its restriction to J × J ¯ J\times \overline {J} is the Poincaré line bundle. We prove that the Fourier-Mukai transform given by P ¯ \overline {P} is an auto-equivalence of the derived category of J ¯ \overline {J} .