{"paper":{"title":"L'id\\'eal de Bernstein d'un arrangement libre d'hyperplans lin\\'eaires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Philippe Maisonobe","submitted_at":"2016-10-06T14:25:20Z","abstract_excerpt":"Let $ V $ a vector space of dimension $n$. A family $ \\{H_1, \\ldots, H_p \\} $ of vectorial hyperplans $V$ defines an arrangement $ {\\cal A} $ of $ V $. For $ i \\in \\{ 1, \\ldots, p \\} $, let $ l_i $ be a linear form on $V$ with $H_i$ as kernel. We denote by $A_V ({\\bf C}) $, the Weyl algebra of algebraic differential operators on $V$. Following J. Bernstein, the ideal constituted by polynomials $ b \\in {\\bf C} [s_1, \\ldots, s_p] $ such that : $$ \\; \\; b (s_1, \\ldots, s_p) \\, l_1^{s_1} \\ldots l_p^{s_p} \\in A_n ({\\bf C}) [s_1, \\ldots, s_p] \\, l_1^ {s_1 + 1} \\ldots l_p^{s_p + 1} \\; , $$ is not red"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03356","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"}