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

## TL;DR

This paper corrects previous mistakes regarding the splitting conditions of Lazarsfeld-Mukai bundles of rank 2 on K3 surfaces and provides refined results and applications related to their splitting types.

## Contribution

It corrects earlier inaccuracies and extends the understanding of splitting conditions for Lazarsfeld-Mukai bundles on K3 surfaces, especially on quartic hypersurfaces.

## Key findings

- Corrected previous mistakes in splitting conditions
- Provided refined splitting types on quartic hypersurfaces
- Applied results to broader contexts

## Abstract

In this paper, we say that a rank 2 bundle splits if it is given by an extension of two line bundles. In the previous works, we gave a necessary condition for Lazarsfeld-Mukai bundles of rank 2 to split, under a numerical condition ([W2], Theorem 3.1). We gave the splitting types of them on a smooth quartic hypersurface in P3 ([W2], 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 [W2].