GV-sheaves, Fourier-Mukai transform, and generic vanishing
By Giuseppe Pareschi, Mihnea Cristian Popa. 2006
114 citations recorded by the source corpus.
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 gives various other generic vanishing results, by reduction to standard vanishing theorems. We further use our criterion in order to address some examples related to generic vanishing on higher rank moduli spaces.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c1c2f49ae9890bdb6e44fc938c823d983a6e55bb
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- GENERIC VANISHING THEORY VIA MIXED HODGE MODULES (2011, background): “ly those E ∈ Db coh(OA) for which RΦP(E) ∈ cD ≤0 coh(OAb), and that the Fourier-Mukai and duality functors satisfy the exchange formula (RΦPE)∨ ≃ RΦP−1(E∨)[g] for any object E in Db coh(OA) (see e.g. [PP11] Lemma 2.2). Observing that P and P−1 differ only by multiplication by −1, the statement follow”
- Unitary local systems, multiplier ideals, and polynomial periodicity of Hodge numbers (2006, background): “t preprint [Li6] which appeared before this revision was made. (b) The size of sets similar-looking to Vq i have been considered from the point of view of the Fourier-Mukai transform by Pareschi-Popa [PP]. For example, for X a smooth projective variety of dimension nand Albanese dimension n−k, [PP]-”