Mathematical Research Letters

Volume 18 (2011)

Number 6

Cohomology of line bundles on compactified Jacobians

Pages: 1215 – 1226



D. Arinkin (Department of Mathematics, University of North Carolina, Chapel Hill, NC, U.S.A.)


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.

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