Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Autoduality of compactified Jacobians for curves with plane singularities


Author: Dima Arinkin
Journal: J. Algebraic Geom. 22 (2013), 363-388
DOI: https://doi.org/10.1090/S1056-3911-2012-00596-7
Published electronically: September 27, 2012
MathSciNet review: 3019453
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Abstract | References | Additional Information

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


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Additional Information

Dima Arinkin
Affiliation: Department of mathematics, University of North Carolina, Chapel Hill, North Carolina
Address at time of publication: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53701
Email: arinkin@email.unc.edu

DOI: https://doi.org/10.1090/S1056-3911-2012-00596-7
Received by editor(s): August 7, 2010
Received by editor(s) in revised form: February 27, 2011
Published electronically: September 27, 2012
Additional Notes: Supported in part by the Alfred P. Sloan Foundation under the Sloan Research Fellowship program.

American Mathematical Society