{"paper":{"title":"Explicit Brill-Noether-Petri general curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Bruno, Enrico Arbarello, Gavril Farkas, Giulia Sacc\\`a","submitted_at":"2015-11-23T17:19:28Z","abstract_excerpt":"Let $p_1,\\dots, p_9$ be the points in $\\mathbb A^2(\\mathbb Q)\\subset \\mathbb P^2(\\mathbb Q)$ with coordinates $$(-2,3),(-1,-4),(2,5),(4,9),(52,375), (5234, 37866),(8, -23), (43, 282), \\Bigl(\\frac{1}{4}, -\\frac{33}{8} \\Bigr)$$ respectively.\n  We prove that, for any genus $g$, a plane curve of degree $3g$ having a $g$-tuple point at $p_1,\\dots, p_8$, and a $(g-1)$-tuple point at $p_9$, and no other singularities, exists and is a Brill-Noether general curve of genus $g$, while a general curve in that $g$-dimensional linear system is a Brill-Noether-Petri general curve of genus $g$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07321","kind":"arxiv","version":3},"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"}