GV-sheaves, Fourier-Mukai transform, and generic vanishing
GV-sheaves, Fourier-Mukai transform, and generic vanishing
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DOI：
10.1353/ajm.2011.0000
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发表时间：
2006-08
影响因子：
1.7
通讯作者：
G. Pareschi;M. Popa
中科院分区：
文献类型：
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作者：
G. Pareschi;M. Popa
我们证明了通用消失的形式标准，该标准由格林和拉扎斯菲尔德发起并由哈康进一步追求，但在任意傅里叶-穆凯对应的背景下。对于光滑射影簇，我们应用它来推导与 nef 线丛相关的伴随丛的 Kodaira 型泛型消失定理，并且实际上是乘数理想滑轮的更一般的泛型 Nadel 型消失定理。仍然在皮卡德簇的背景下，相同的方法通过简化为标准消失定理给出了各种其他通用消失结果。我们进一步使用我们的标准来解决与高阶模空间上的泛型消失相关的一些示例。
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.