{"paper":{"title":"Unstable Lazarsfeld-Mukai bundles of rank 2 on a certain K3 surface of Picard number 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AG","authors_text":"Kenta Watanabe","submitted_at":"2017-06-30T08:23:25Z","abstract_excerpt":"Let $g$ and $c$ be any integers satisfying $g\\geq3$ and $0\\leq c\\leq \\lfloor\\frac{g-1}{2}\\rfloor$. 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00643","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}