Generic vanishing and Fourier-Mukai transforms
I will describe some very general results concerning the vanishing of
cohomology sheaves in Fourier-Mukai transforms, and the generic
cohomology groups. Such results can be applied in various directions
of them largely unexplored). I will outline some selected applications
abelian and irregular varieties:
Joint work with Mihnea Popa.
- the study of certain subvarieties
ppav's, which are closely related to subvarieties representing minimal
- an improvement of Green-Lazarsfeld generic
- a higher dimensional Castelnuovo-de Franchis inequality.