{"paper":{"title":"Linear stability and stability of Lazarsfeld-Mukai bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, H. Torres-Lopez","submitted_at":"2017-05-18T23:13:55Z","abstract_excerpt":"Let $C$ be a smooth irreducible projective curve and let $(L,H^0(C,L))$ be a complete and generated linear series on $C$. Denote by $M_L$ the kernel of the evaluation map $H^0(C,L)\\otimes\\mathcal O_C\\to L$. The exact sequence $0\\to M_L\\to H^0(C,L)\\otimes\\mathcal O_C\\to L\\to 0$ fits into a commutative diagram that we call the Butler's diagram. This diagram induces in a natural way a multiplication map on global sections $m_W: W^{\\vee}\\otimes H^0(K_C)\\to H^0(S^{\\vee}\\otimes K_C)$, where $W\\subseteq H^0(C,L)$ is a subspace and $S^{\\vee}$ is the dual of a subbundle $S\\subset M_L$. When the subbund"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.06829","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"}