Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of Picard number 2

06/30/2017

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by   Kenta Watanabe, et al.

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Let g and c be any integers satisfying g≥3 and 0≤ c≤g-1/2. It is known that there exists a polarized K3 surface (X,H) such that X is a K3 surface of Picard number 2, and H is a very ample line bundle on X of sectional genus g and Clifford index c, by Johnsen and Knutsen([J-K] and [Kn]). In this paper, we give a necessary and sufficient condition for a Lazarsfeld-Mukai bundles of rank 2 associated with a smooth curve C belonging to the linear system |H| and a base point free pencil on C not to be H-slope stable.