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

Kenta Watanabe ()
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Kenta Watanabe: Nihon University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 55-65

Abstract: 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.

Keywords: K3 surface; line bundle; Lazarsfeld-Mukai bundle; slope stability; Brill-Noether theory; 14J28; 14J60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0384-x

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