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- W2952179907 abstract "In this paper we give two explicit relations among 1-cycles modulo rational equivalence on a smooth cubic hypersurfaces $X$. Such a relation is given in terms of a (pair of) curve(s) and its secant lines. As the first application, we reprove Paranjape's theorem that $mathrm{CH}_1(X)$ is always generated by lines and that it is isomorphic to $Z$ if the dimension of $X$ is at least 5. Another application is to the intermediate jacobian of a cubic threefold $X$. To be more precise, we show that the intermediate jacobian of $X$ is naturally isomorphic to the Prym-Tjurin variety constructed from the curve parameterizing all lines meeting a given curve on $X$. The incidence correspondences play an important role in this study. We also give a description of the Abel-Jacobi map for 1-cycles in this setting." @default.
- W2952179907 created "2019-06-27" @default.
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- W2952179907 date "2011-02-12" @default.
- W2952179907 modified "2023-10-17" @default.
- W2952179907 title "On relations among 1-cycles on cubic hypersurfaces" @default.
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- W2952179907 doi "https://doi.org/10.48550/arxiv.1102.2550" @default.
- W2952179907 hasPublicationYear "2011" @default.
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