{"paper":{"title":"Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hirotachi Abo, Maria Chiara Brambilla","submitted_at":"2008-09-28T11:39:57Z","abstract_excerpt":"Let $X_{m,n}$ be the Segre-Veronese variety $\\mathbb{P}^m \\times \\mathbb{P}^n$ embedded by the morphism given by $\\mathcal{O}(1,2)$. In this paper, we provide two functions $\\underline{s}(m,n)\\le \\bar{s}(m,n)$ such that the $s^{\\mathrm{th}}$ secant variety of $X_{m,n}$ has the expected dimension if $s \\leq \\underline{s}(m,n)$ or $ \\bar{s}(m,n) \\leq s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4837","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"}