Autoduality of compactified Jacobians for curves with plane singularities

Abstract

Let C be an integral projective curve with planar singularities. Consider its Jacobian J and the compactified Jacobian J'. We construct a flat family P of Cohen-Macaulay sheaves on J' parametrized by J'; over J, the family P is the Poincare line bundle. We prove that the Fourier-Mukai transform given by P is an auto-equivalence of the derived category of J'.

20 pages. Version 2: Minor modifications, two references added

References in corpus (3)

• Langlands duality for Hitchin systems
• Isospectral commuting variety and the Harish-Chandra D-module
• Cohomology of line bundles on compactified Jacobians

Cited by in corpus (5)

• Global topology of the Hitchin system
• Singular Geometry and Higgs Bundles in String Theory
• Construction of the Poincare sheaf for higher genus curves
• Construction of the Poincaré sheaf on the stack of rank two Higgs bundles of ${\mathbf{P}}^1$
• Mirror of Orbifold Singularities in the Hitchin Fibration: the case $({\text{SL}}_n,{\text{PGL}}_n)$