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 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 W2d. If the Brill-Noether number is negative, then we prove that any on any smooth, irreducible curve in L is contained in a 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. © 2013 London Mathematical Society.

Lelli-Chiesa, M. (2013). Stability of rank-3 Lazarsfeld-Mukai bundles on K3 surfaces. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 107(2), 451-479 [10.1112/plms/pds087].

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

Lelli-Chiesa M.
2013-01-01

Abstract

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 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 W2d. If the Brill-Noether number is negative, then we prove that any on any smooth, irreducible curve in L is contained in a 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. © 2013 London Mathematical Society.
Lelli-Chiesa, M. (2013). Stability of rank-3 Lazarsfeld-Mukai bundles on K3 surfaces. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 107(2), 451-479 [10.1112/plms/pds087].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/360174
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