Stability of rank-3 Lazarsfeld-Mukai bundles on K3 surfaces

Given an ample line bundle L on a K3 surface S, we study the slope stability with respect to L of rank-3 Lazarsfeld-Mukai bundles associated with complete, base point free nets of type g^2_d on curves C in the linear system |L|. When d is large enough and C is general, we obtain a dimensional statem...

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Bibliographic Details
Published in:arXiv.org 2013-02
Main Author: Lelli-Chiesa, Margherita
Format: Article
Language:English
Subjects:
Bundles
Bundling
Slope stability
Surface stability
Online Access:Get full text
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Summary:Given an ample line bundle L on a K3 surface S, we study the slope stability with respect to L of rank-3 Lazarsfeld-Mukai bundles associated with complete, base point free nets of type g^2_d on curves C in the linear system |L|. When d is large enough and C is general, we obtain a dimensional statement for the variety W^2_d(C). If the Brill-Noether number is negative, we prove that any g^2_d on any smooth, irreducible curve in |L| is contained in a g^r_e which is induced from a line bundle on S, thus answering a conjecture of Donagi and Morrison. Applications towards transversality of Brill-Noether loci and higher rank Brill-Noether theory are then discussed.
ISSN:2331-8422
DOI:10.48550/arxiv.1112.2938