TY - JOUR
T1 - GV-sheaves, fourier-mukai transform, and generic vanishing
AU - Pareschi, Giuseppe
AU - Popa, Mihnea
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
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U2 - 10.1353/ajm.2011.0000
DO - 10.1353/ajm.2011.0000
M3 - Article
AN - SCOPUS:79251604277
SN - 0002-9327
VL - 133
SP - 235
EP - 271
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 1
ER -