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Relative Fourier-Mukai transforms for Weierstrass fibrations, abelian schemes and Fano fibrations

Thursday 20th January 2011 - 15:30 to 16:30
INI Seminar Room 1
Since its introduction by Mukai, the theory of integral functors and Fourier-Mukai transforms have been important tools in the study of the geometry of varieties and moduli spaces.

Working with a fibered scheme over a base $T$ it is quite natural to look at the group of $T$-linear autoequivalences. The description of this group seems a hard problem. We will restrict ourselves to the subgroup given by relative Fourier-Mukai transforms. In this talk, I will explain how for a projective fibration the knowledge of the structure of the group of autoequivalences of its fibres and the properties of relative integral functors provide a machinery to study that subgroup. I will work out the case of a Weierstrass fibrations and report about the results for abelian schemes and Fano or anti-Fano fibrations.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons