{"paper":{"title":"Combinatorics of line arrangements and polynomial vector fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Beno\\^it Guerville-Ball\\'e, Juan Viu-Sos","submitted_at":"2014-11-10T22:56:26Z","abstract_excerpt":"Let $\\mathcal{A}$ be a real line arrangement and $\\mathcal{D}(\\mathcal{A})$ the module of $\\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\\mathcal{A}$ as an invariant set. We first characterize polynomial vector fields having an infinite number of invariant lines. Then we prove that the minimal degree of polynomial vector fields fixing only a finite set of lines in $\\mathcal{D}(\\mathcal{A})$ is not determined by the combinatorics of $\\mathcal{A}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2653","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"}