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SUMMARY:Autoduality and Fourier-Mukai transform for compactified Jacobians
  of singular curves
DTSTART:20120927T151500
DTEND:20120927T170000
DTSTAMP:20261005T011459Z
UID:0fabe5a0da4034425b92a418cda94b9edb1cc633e41fa8e2c8e69929
CATEGORIES:Conferences - Seminars
DESCRIPTION:Filippo Viviani\, Roma Tre University\nTo every reduced projec
 tive curve X with locally planar singularities one can associate\, followi
 ng Esteves\, many fine compactified Jacobians\, depending on the choice of
  a polarization on X\, each of which yields a modular compatification of t
 he generalized Jacobian of X. We prove that for each such fine compactifie
 d Jacobian of X\, there exists a natural Poincaré sheaf such that the ass
 ociated Fourier-Mukai transform is an autoquivalence of its derived catego
 ry of coherent sheaves\, generalizing a previous result of Arinkin for int
 egral curves. As a consequence\, we prove that algebraic equivalence and n
 umerical 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 sc
 heme of any fine compactified Jacobian of X\, generalizing previous result
 s of Arinkin\, Esteves\, Gagne\, Kleiman.  If time permits\, we will expl
 ain how these results can be seen as an instance of the classical limit of
  the (conjectural) geometric Langlands duality for the general linear grou
 p. This is a joint work with M. Melo and A. Rapagnetta.
LOCATION:CM 1 100 http://plan.epfl.ch/?lang=fr&room=cm1+100
STATUS:CONFIRMED
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