GV-sheaves, fourier-mukai transform, and generic vanishing

Giuseppe Pareschi*, Mihnea Popa

*Corresponding author for this work

Research output: Contribution to journalArticle

34 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)235-271
Number of pages37
JournalAmerican Journal of Mathematics
Volume133
Issue number1
DOIs
StatePublished - Feb 1 2011

ASJC Scopus subject areas

  • Mathematics(all)

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