{"paper":{"title":"Matrix factorizations and curves in $\\mathbb{P}^4$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Fabio Tanturri, Frank-Olaf Schreyer","submitted_at":"2016-11-11T11:58:52Z","abstract_excerpt":"Let $C$ be a curve in $\\mathbb{P}^4$ and $X$ be a hypersurface containing it. We show how it is possible to construct a matrix factorization on $X$ from the pair $(C,X)$ and, conversely, how a matrix factorization on $X$ leads to curves lying on $X$. We use this correspondence to prove the unirationality of the Hurwitz space $\\mathcal{H}_{12,8}$ and the uniruledness of the Brill-Noether space $\\mathcal{W}^1_{13,9}$. Several unirational families of curves of genus $16 \\leq g \\leq 20$ in $\\mathbb{P}^4$ are also exhibited."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03669","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"}