{"paper":{"title":"The secant line variety to the varieties of reducible plane curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Alessandro Gimigliano, Anthony V. Geramita, Maria Virginia Catalisano, Yong-Su Shin","submitted_at":"2014-04-15T13:54:37Z","abstract_excerpt":"Let $\\lambda =[d_1,\\dots,d_r]$ be a partition of $d$. Consider the variety $\\mathbb{X}_{2,\\lambda} \\subset \\mathbb{P}^N$, $N={d+2 \\choose 2}-1$, parameterizing forms $F\\in k[x_0,x_1,x_2]_d$ which are the product of $r\\geq 2$ forms $F_1,\\dots,F_r$, with deg$F_i = d_i$. We study the secant line variety $\\sigma_2(\\mathbb{X}_{2,\\lambda})$, and we determine, for all $r$ and $d$, whether or not such a secant variety is defective. Defectivity occurs in infinitely many \"unbalanced\" cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3911","kind":"arxiv","version":2},"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"}