{"paper":{"title":"Schemes supported on the singular locus of a hyperplane arrangement in $\\mathbb P^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"H. Schenck, J. Migliore, U. Nagel","submitted_at":"2019-08-11T17:21:12Z","abstract_excerpt":"We introduce the use of liaison addition to the study of hyperplane arrangements. For an arrangement, $\\mathcal A$, of hyperplanes in $\\mathbb P^n$, $\\mathcal A$ is free if $R/J$ is Cohen-Macaulay, where $J$ is the Jacobian ideal of $\\mathcal A$. Terao's conjecture says that freeness of $\\mathcal A$ is determined by the combinatorics of the intersection lattice of $\\mathcal A$. We study the Cohen-Macaulayness of three other ideals, all unmixed, that are closely related to $\\mathcal A$. Let $\\overline J = \\mathfrak q_1 \\cap \\dots \\cap \\mathfrak q_s$ be the intersection of height two primary com"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03939","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}