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:
  1. the study of certain subvarieties of ppav's, which are closely related to subvarieties representing minimal cohomology classes;
  2. an improvement of Green-Lazarsfeld generic vanishing theorem;
  3. a higher dimensional Castelnuovo-de Franchis inequality.
Joint work with Mihnea Popa.