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

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.