Cohomology of line bundles on compactified Jacobians

Let $C$ be an integral projective curve with planar singularities. For the compactified Jacobian $\oJ$ of $C$, we prove that topologically trivial line bundles on $\oJ$ are in one-to-one correspondence with line bundles on $C$ (the autoduality conjecture), and compute the cohomology of $\oJ$ 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 $\oJ$ is fully faithful.

Full Text (PDF format)

Published 20 February 2012