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SUMMARY:Autoduality and Fourier-Mukai transform for compactified Jacobians
  of singular curves
DTSTART:20120927T151500
DTEND:20120927T170000
DTSTAMP:20261005T110913Z
UID:14571b6ba45925811830593a49e787e4cc3ac8be5cf756a9b8c99223
CATEGORIES:Conferences - Seminars
DESCRIPTION:Filippo Viviani\, University of Rome Tre\nTo every reduced pro
 jective curve X with locally planar singularities one can associate\, foll
 owing Esteves\, many fine compactified Jacobians\, depending on the choice
  of a polarization on X\, each of which yields a modular compatification o
 f the generalized Jacobian of X. We prove that for each such fine compacti
 fied Jacobian of X\, there exists a natural Poincaré sheaf such that the 
 associated Fourier-Mukai transform is an autoquivalence of its derived cat
 egory of coherent sheaves\, generalizing a previous result of Arinkin for 
 integral curves. As a consequence\, we prove that algebraic equivalence an
 d numerical equivalence coincide on any fine compactified Jacobian and tha
 t\, moreover\, there is a canonical isomorphism (called autoduality) betwe
 en the generalized Jacobian of X and the connected component of the Picard
  scheme of any fine compactified Jacobian of X\, generalizing previous res
 ults of Arinkin\, Esteves\, Gagne\, Kleiman.  If time permits\, we will e
 xplain how these results can be seen as an instance of the classical limit
  of the (conjectural) geometric Langlands duality for the general linear g
 roup. This is a joint work with M. Melo and A. Rapagnetta.
LOCATION:CM 1 100 http://plan.epfl.ch/?lang=fr&room=cm+1+100
STATUS:CONFIRMED
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