{"paper":{"title":"The Noether-Lefschetz locus of surfaces in toric threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonella Grassi, Ugo Bruzzo","submitted_at":"2015-08-08T12:41:39Z","abstract_excerpt":"The Noether-Lefschetz theorem asserts that any curve in a very general surface $X$ in $\\mathbb P^3$ of degree $d \\geq 4$ is a restriction of a surface in the ambient space, that is, the Picard number of $X$ is $1$. We proved previously that under some conditions, which replace the condition $d \\geq 4$, a very general surface in a simplicial toric threefold $\\mathbb P_\\Sigma$ (with orbifold singularities) has the same Picard number as $\\mathbb P_\\Sigma$. Here we define the Noether-Lefschetz loci of quasi-smooth surfaces in $\\mathbb P_\\Sigma$ in a linear system of a Cartier ample divisor with re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01895","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"}