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SUMMARY:Partial Fourier-Mukai transform for algebraically integrable syste
 ms
DTSTART:20140310T151500
DTEND:20140310T170000
DTSTAMP:20260407T045713Z
UID:820a5e497705f5b67cdba8d104840dabe661c4b49fb15bc70c0e417b
CATEGORIES:Conferences - Seminars
DESCRIPTION:Roman Fedorov\, Kansas State\nThe celebrated Fourier-Mukai tra
 nsform is an equivalence between the\nderived category of an abelian varie
 ty and that of the dual abelian\nvariety. Recently there have been a lot o
 f interest in Fourier-Mukai\ntransforms for singular degenerations of abel
 ian varieties\, e.g.\, for\nJacobians of singular curves. However\, very l
 ittle is known beyond the\nJacobian case. In a joint work with D. Arinkin 
 we suggest a different\nsetup. Let p:X->B be a flat morphism of smooth com
 plex varieties with\nintegral projective fibers. We also assume that X is 
 symplectic and the\nsmooth locus of each fiber is Lagrangian (thus\, we do
  not assume that\nthe fibers are smooth). We argue that in this case p:X->
 B is an\nalgebraically completely integrable system. We construct the smoo
 th part\nof the 'dual integrable system' and construct the corresponding p
 artial\nFourier-Mukai transform. Applications to Hitchin systems will be d
 iscussed.
LOCATION:MAA331 http://plan.epfl.ch/?lang=fr&room=MA+A331
STATUS:CONFIRMED
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