On the splitting of Lazarsfeld-Mukai bundles on K3 surfaces II

In the previous works, we gave a necessary condition for Lazarsfeld-Mukai bundles of rank 2 on a K3 surface X to be given by an extension of two line bundles, under a numerical condition ([10], Theorem 3.1). Moreover, we have classified line bundles which appear in such an extension, in the case where X is a smooth quartic hypersurface in P-3 ([10], Proposition 3.1) as a corollary of it. However, the assertion of it contains a few mistakes. In this paper, we correct them, and give an application of the results in [10]. (C) 2018 Elsevier Inc. All rights reserved.