Autoduality and Fourier-Mukai transform for compactified Jacobians of singular curves

Event details
Date | 27.09.2012 |
Hour | 15:15 › 17:00 |
Speaker | Filippo Viviani, University of Rome Tre |
Location | |
Category | Conferences - Seminars |
To every reduced projective curve X with locally planar singularities one can associate, following Esteves, many fine compactified Jacobians, depending on the choice of a polarization on X, each of which yields a modular compatification of the generalized Jacobian of X. We prove that for each such fine compactified Jacobian of X, there exists a natural Poincaré sheaf such that the associated Fourier-Mukai transform is an autoquivalence of its derived category of coherent sheaves, generalizing a previous result of Arinkin for integral curves. As a consequence, we prove that algebraic equivalence and numerical equivalence coincide on any fine compactified Jacobian and that, moreover, there is a canonical isomorphism (called autoduality) between the generalized Jacobian of X and the connected component of the Picard scheme of any fine compactified Jacobian of X, generalizing previous results of Arinkin, Esteves, Gagne, Kleiman. If time permits, we will explain how these results can be seen as an instance of the classical limit of the (conjectural) geometric Langlands duality for the general linear group. This is a joint work with M. Melo and A. Rapagnetta.
Practical information
- General public
- Free
- This event is internal
Organizer
- Tamas Hausel, Chair of Geometry
Contact
- tamas.hausel@epfl.ch