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- W4288104513 abstract "Griffiths and Harris showed in 1978 that if E is a rank n vector bundle on a smooth projective variety of dimension n, and if s is a section of E vanishing simply on a finite set Z, then any section of (K_X + det E) vanishing at all but one of the points of Z must also vanish on the remaining one. This generalizes the classical theorem of Cayley-Bacharach, which appears when E is a direct sum of line bundles on projective space. In a recent paper, Mu-Lin Li proposed an extension allowing for the possibility that the zero-locus of s has positive dimensional components, but his result requires a splitting hypothesis that in practice is rarely satisfied. We show that multiplier ideals lead to a quite clean statement in the case of excess vanishing. Along the way, we give simplified and somewhat strengthened accounts of results of Tan-Viehweg and Sun." @default.
- W4288104513 created "2022-07-28" @default.
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- W4288104513 date "2019-09-18" @default.
- W4288104513 modified "2023-09-28" @default.
- W4288104513 title "Cayley-Bacharach theorems with excess vanishing" @default.
- W4288104513 doi "https://doi.org/10.48550/arxiv.1909.08493" @default.
- W4288104513 hasPublicationYear "2019" @default.
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