{"paper":{"title":"Complete intersections in simplicial toric varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CO"],"primary_cat":"math.AC","authors_text":"Ignacio Garc\\'ia-Marco, Isabel Bermejo","submitted_at":"2013-02-27T10:02:41Z","abstract_excerpt":"Given a set $\\mathcal A = \\{a_1,\\ldots,a_n\\} \\subset \\mathbb{N}^m$ of nonzero vectors defining a simplicial toric ideal $I_{\\mathcal A} \\subset k[x_1,...,x_n]$, where $k$ is an arbitrary field, we provide an algorithm for checking whether $I_{\\mathcal A}$ is a complete intersection. This algorithm does not require the explicit computation of a minimal set of generators of $I_{\\mathcal A}$. The algorithm is based on the application of some new results concerning toric ideals to the simplicial case. For homogenous simplicial toric ideals, we provide a simpler version of this algorithm. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6706","kind":"arxiv","version":4},"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"}