{"paper":{"title":"Varieties of Picard rank one as components of ample divisors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrea Luigi Tironi","submitted_at":"2014-02-04T19:35:11Z","abstract_excerpt":"Let $\\mathcal{V}$ be an integral normal complex projective variety of dimension $n\\geq 3$ and denote by $\\mathcal{L}$ an ample line bundle on $\\mathcal{V}$. By imposing that the linear system $|\\mathcal{L}|$ contains an element $A=A_{1}+...+A_{r}, r\\geq 1$, where all the $A_{i}$'s are distinct effective Cartier divisors with Pic$(A_i)=\\mathbb{Z}$, we show that such a $\\mathcal{V}$ is as special as the components $A_i$ of $A\\in |\\mathcal{L}|$. After making a list of some consequences about the positivity of the components $A_i$, we characterize pairs $(\\mathcal{V}, \\mathcal{L})$ as above when e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0839","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"}