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Lazarsfeld-Mukai Bundles of Rank 2 on a Polarized K3 Surface of Low Genus

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Abstract

Let X be a K3 surface and let H be a very ample line bundle on X of sectional genus g ≤ 9. In this paper, we characterize the destabilizing sheaf of the Lazarsfeld-Mukai bundle EC,Z of rank 2 associated with a smooth curve C ∈ |H| and a base point free divisor Z on C with h0(OC(Z)) = 2, in the case where it is not H-slope stable.

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Acknowledgement

The author would like to thank the referee for some helpful comments. The author is partially supported by Grant-in-Aid for Scientific Research (16K05101), Japan Society for the Promotion of Science.

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Authors and Affiliations

  1. College of Science and Technology, Nihon University, 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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Watanabe, K. Lazarsfeld-Mukai Bundles of Rank 2 on a Polarized K3 Surface of Low Genus. Indian J Pure Appl Math 51, 55–65 (2020). https://doi.org/10.1007/s13226-020-0384-x

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  • DOI: https://doi.org/10.1007/s13226-020-0384-x

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