{"paper":{"title":"Star Configurations are Set-Theoretic Complete Intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Stefan Tohaneanu","submitted_at":"2015-07-20T22:12:40Z","abstract_excerpt":"Let $\\mathcal A\\subset\\mathbb P^{k-1}$ be a rank $k$ arrangement of $n$ hyperplanes, with the property that any $k$ of the defining linear forms are linearly independent (i.e., $\\mathcal A$ is called $k-$generic). We show that for any $j=0,\\ldots,k-2$, the subspace arrangement with defining ideal generated by the $(n-j)-$fold products of the defining linear forms of $\\mathcal A$ is a set-theoretic complete intersection, which is equivalent to saying that star configurations have this property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05667","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"}