{"paper":{"title":"Hodge locus and Brill-Noether type locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.AG","authors_text":"Ananyo Dan, Indranil Biswas","submitted_at":"2016-09-04T23:17:57Z","abstract_excerpt":"Given a family $\\pi:\\mc{X} \\rightarrow B$ of smooth projective varieties, a closed fiber $\\mc{X}_o$ and an invertible sheaf $\\mc{L}$ on $\\mc{X}_o$, we compare the Hodge locus in $B$ corresponding to the Hodge class $c_1(\\mc{L})$ with the locus of points $b\\,\\in\\, B$ such that $\\mc{L}$ deforms to an invertible sheaf $\\mc{L}_b$ on $\\mc{X}_b$ with at least $h^0(\\mc{L})$--dimensional space of global sections (it is a Brill-Noether type locus associated to $\\mc{L}$). We finally give an application by comparing the Brill-Noether locus to a family of curves on a surface passing through a fixed set of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00997","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"}