skip to content
 

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

Presented by: 
C Lopez Martin [Salamanca]
Date: 
Thursday 20th January 2011 - 15:30 to 16:30
Venue: 
INI Seminar Room 1
Abstract: 
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.

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
University of Cambridge Research Councils UK
    Clay Mathematics Institute The Leverhulme Trust London Mathematical Society Microsoft Research NM Rothschild and Sons