{"paper":{"title":"Focal schemes to families of secant spaces to canonical curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Michael Hoff","submitted_at":"2017-10-05T08:58:45Z","abstract_excerpt":"This article is a generalisation of results of Ciliberto and Sernesi. For a general canonically embedded curve $C$ of genus $g\\geq 5$, let $d\\le g-1$ be an integer such that the Brill--Noether number $\\rho(g,d,1)=g-2(g-d+1)\\geq 1$. We study the family of $d$-secant $\\mathbb{P}^{d-2}$'s to $C$ induced by the smooth locus of the Brill--Noether locus $W^1_d(C)$. Using the theory of foci and a structure theorem for the rank one locus of special $1$-generic matrices by Eisenbud and Harris, we prove a Torelli-type theorem for general curves by reconstructing the curve from its Brill--Noether loci $W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01923","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"}