Cohomology of line bundles on compactified jacobians

Abstract

Let C be an integral projective curve with planar singularities. For the compactified Jacobian J of C, we prove that topologically trivial line bundles on J are in one-to-one correspondence with line bundles on C (the autoduality conjecture), and compute the cohomology of J with coefficients in these line bundles. We also show that the natural Fourier-Mukai functor from the derived category of quasi-coherent sheaves on J (where J is the Jacobian of X) to that of quasi-coherent sheaves on J is fully faithful. © International Press 2012.