Partial Fourier-Mukai transform for algebraically integrable systems
Event details
| Date | 10.03.2014 |
| Hour | 15:15 › 17:00 |
| Speaker | Roman Fedorov, Kansas State |
| Location | |
| Category | Conferences - Seminars |
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
Fourier-Mukai transform. Applications to Hitchin systems will be discussed.
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
Fourier-Mukai transform. Applications to Hitchin systems will be discussed.
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