{"paper":{"title":"Invariants of the Brill-Noether curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Abel Castorena, Alberto L\\'opez Mart\\'in, Montserrat Teixidor i Bigas","submitted_at":"2014-03-28T19:11:03Z","abstract_excerpt":"For a projective nonsingular curve of genus $g$, the Brill-Noether locus $W^r_d(C)$ parametrizes line bundles of degree $d$ over $C$ with at least $r+1$ sections. When the curve is generic and the Brill-Noether number $\\rho(g,r,d)$ equals $1$, one can then talk of the \\emph{Brill-Noether curve}. In this paper, we explore the first two invariants of this curve, giving a new way of calculating the genus of this curve and computing its gonality when $C$ has genus 5."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7489","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"}