ACM bundles of rank 2 on quartic hypersurfaces in $${\mathbb {P}}^3$$ P 3 and Lazarsfeld-Mukai bundles

Kenta Watanabe ()
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Kenta Watanabe: Nihon University, College of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2023, vol. 54, issue 1, 38-48

Abstract: Abstract Let X be a smooth quartic hypersurface in $$\mathbb {P}^3$$ P 3 . By the Brill-Noether theory of curves on K3 surfaces, if a rank 2 aCM bundle on X is globally generated, then it is the Lazarsfeld-Mukai bundle $$E_{C,Z}$$ E C , Z associated with a smooth curve C on X and a base point free pencil Z on C. In this paper, we will focus on the classification of such bundles on X to investigate aCM bundles of rank 2 on X. Concretely, we will give a necessary condition for a rank 2 vector bundle of type $$E_{C,Z}$$ E C , Z to be indecomposable initialized and aCM, in the case where the class of C in $${{\,\mathrm{Pic}\,}}(X)$$ Pic ( X ) is contained in the sublattice of rank 2 generated by the hyperplane class of X and a non-trivial initialized aCM line bundle on X.

Keywords: ACM bundles; Quartic hypersurface; Lazarsfeld-Mukai bundle; Brill-Noether theory; 14J28; 14J60; 14H60 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13226-022-00227-8

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