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# Partial Fourier-Mukai transform for algebraically integrable systems

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Roman Fedorov (Kansas State University), z.Z. MPIM - Seminar Algebraic Geometry (SAG)

What Seminar May 15, 2014 from 10:30 am to 11:30 am Bonn, Hörsaal MPI, Vivatsgasse 7 Sachinidis vCal iCal

The celebrated Fourier-Mukai transform is an equivalence between the derived category of an abelian variety and that of the dual abelian variety. Recently there have been a lot of interest in Fourier-Mukai transforms for singular degenerations of abelian varieties, e.g., for Jacobians of singular curves. However, very little is known beyond the Jacobian case. In a joint work with D. Arinkin we suggest a different setup. Let p:X->B be a flat morphism of smooth complex varieties with integral projective fibers. We also assume that X is symplectic and the smooth locus of each fiber is Lagrangian (thus, we do not assume that the fibers are smooth). We argue that in this case p:X->B is an algebraically completely integrable system. We construct the smooth part of the 'dual integrable system' and construct the corresponding partial