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The characterization of aCM line bundles on quintic hypersurfaces in \(\mathbb {P}^3\)

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Abstract

Let X be a smooth quintic hypersurface in \(\mathbb {P}^3\), let C be a smooth hyperplane section of X, and let \(H=\mathcal {O}_X(C)\). In this paper, we give a necessary and sufficient condition for the line bundle given by a non-zero effective divisor on X to be initialized and aCM with respect to H.

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Acknowledgements

The author would like to thank the referee for some helpful comments.

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Authors and Affiliations

  1. Nihon University, College of Science and Technology, 7-24-1 Narashinodai Funabashi city, Chiba, 274-8501, Japan

    Kenta Watanabe

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  1. Kenta Watanabe
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Correspondence to Kenta Watanabe.

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Communicated by Herr Greb.

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Watanabe, K. The characterization of aCM line bundles on quintic hypersurfaces in \(\mathbb {P}^3\). Abh. Math. Semin. Univ. Hambg. 91, 179–197 (2021). https://doi.org/10.1007/s12188-021-00250-2

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