# GV-sheaves, Fourier-Mukai transform, and generic vanishing

@article{Pareschi2006GVsheavesFT, title={GV-sheaves, Fourier-Mukai transform, and generic vanishing}, author={Giuseppe Pareschi and Mihnea Cristian Popa}, journal={American Journal of Mathematics}, year={2006}, volume={133}, pages={235 - 271} }

We prove a formal criterion for generic vanishing, in the sense originated by Green and Lazarsfeld and pursued further by Hacon, but in the context of an arbitrary Fourier-Mukai correspondence. For smooth projective varieties we apply this to deduce a Kodaira-type generic vanishing theorem for adjoint bundles associated to nef line bundles, and in fact a more general generic Nadel-type vanishing theorem for multiplier ideal sheaves. Still in the context of the Picard variety, the same method…

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