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