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arXiv · 1503.06682

Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles

Kenta Watanabe
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Abstract

Previously, many people have studied a stability of vector bundles of given rank and Chern classes on algebraic varieties. Recently, we are interested in the slope stability of the rank 2 Lazarsfeld-Mukai bundle $E_{C,Z}$ on a K3 surface $X$ associated to a very ample smooth curve $C$ on $X$ and a base point free pencil $Z$ on $C$ with respect to $\mathcal{O}_X(C)$. In this paper, we will give a sufficient condition for such a Lazarsfeld-Mukai bundle $E_{C,Z}$ to be $\mathcal{O}_X(C)$-slope semistable by ACM line bundles with respect to $\mathcal{O}_X(C)$.

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Kenta Watanabe. 2015-03-23. Slope semistability of rank 2 Lazarsfeld-Mukai bundles on K3 surfaces and ACM line bundles. https://arxiv.org/abs/1503.06682

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