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- W4297581695 abstract "An algebraic variety X is embedded to the order k via a line bundle L if the global sections of L generate all (simultaneous) jets of order k on X or if they separate all zero-dimensional subschemes of length at most k+1. Even though we refer to both situations as higher order embeddings, the first notion (in which case L is said to be k-jet ample) is stronger than the second one (when L is k-very ample). The purpose of this paper is to study higher order embeddings of cyclic coverings pi:Yto X via line bundles given by pulling back sufficiently positive line bundles on X. Given a line bundle L on X, we relate the order of the embedding defined by pi^*L to that of L and of certain rank 1 summands of the vector bundle Ltensorpi_*calo_Y. As expected, the sufficient conditions for pi^*L to be k-jet ample are stronger then the ones needed in order for pi^*L to be k-very ample." @default.
- W4297581695 created "2022-09-30" @default.
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- W4297581695 date "1998-06-29" @default.
- W4297581695 modified "2023-09-26" @default.
- W4297581695 title "Cyclic coverings and higher order embeddings of algebraic varieties" @default.
- W4297581695 doi "https://doi.org/10.48550/arxiv.math/9806153" @default.
- W4297581695 hasPublicationYear "1998" @default.
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