{"paper":{"title":"Remarks on Ruled surfaces and rank two bundles with canonical determinant and 4 sections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Graciela Reyes-Ahumada","submitted_at":"2014-11-15T15:22:57Z","abstract_excerpt":"Let $C$ be a smooth irreducible complex projective curve of genus $g$ and let $B^k(2,K_C)$ be the Brill-Noether loci parametrizing classes of (semi)-stable vector bundles $E$ of rank two with canonical determinant over $C$ with $h^0(C,E)\\geq k$. We show that $B^4(2,K_C)$ it has an irreducible component $\\mathcal B$ of dimension $3g-13$ on a general curve $C$ of genus $g\\geq 8$. Moreover, we show that for the general element $[E]$ of $\\mathcal B$, $E$ fits in a exact sequence $0\\to\\mathcal O_C(D)\\to E\\to K_C(-D)\\to 0$, with $D$ a general effective divisor of degree three, and the corresponding "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4155","kind":"arxiv","version":2},"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"}