{"paper":{"title":"The $\\textbf{nbc}$ minimal complex of supersolvable arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Michele Torielli, Simona Settepanella","submitted_at":"2015-03-19T11:41:26Z","abstract_excerpt":"In this paper we give a very natural description of the bijections between the minimal CW-complex homotopy equivalent to the complement of a supersolvable arrangement $\\mathcal{A}$, the $\\textbf{nbc}$ basis of the Orlik-Solomon algebra associated to $\\mathcal{A}$ and the set of chambers of $\\mathcal{A}$. We use these bijections to get results on the first (co)homology group of the Milnor fiber of $\\mathcal{A}$ and to describe a bijection between the symmetric group and the $\\textbf{nbc}$ basis of the braid arrangement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05721","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"}