{"paper":{"title":"Implicitization of tensor product surfaces in the presence of a generic set of basepoints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Eliana Duarte","submitted_at":"2016-10-12T18:48:19Z","abstract_excerpt":"Given a $4$-dimensional vector subspace $U=\\{ f_{0},\\ldots,f_{3}\\}$ of $H^{0}(\\mathbb{P}^1 \\times \\mathbb{P}^1,\\mathcal{O}(a,b))$, a tensor product surface, denoted by $X_{U}$, is the closure of the image of the rational map $\\lambda_{U}:\\mathbb{P}^1 \\times \\mathbb{P}^1 -\\!\\to \\mathbb{P}^{3}$ determined by $U$. These surfaces arise in geometric modeling and in this context it is useful to know the implicit equation of $X_{U}$ in $\\mathbb{P}^{3}$. In this paper we show that if $U\\subseteq H^{0}(\\mathbb{P}^1 \\times \\mathbb{P}^1,\\mathcal{O}(a,1))$ has a finite set of $r$ basepoints in generic pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03820","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"}