{"paper":{"title":"Modular equalities for complex reflection arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.AG","authors_text":"Clement Radu Popescu, Daniela Anca Macinic, Stefan Papadima","submitted_at":"2014-06-27T10:08:23Z","abstract_excerpt":"We compute the combinatorial Aomoto-Betti numbers $\\beta_p(\\mathcal{A})$ of a complex reflection arrangement. When $\\mathcal{A}$ has rank at least $3$, we find that $\\beta_p(\\mathcal{A})\\le 2$, for all primes $p$. Moreover, $\\beta_p(\\mathcal{A})=0$ if $p>3$, and $\\beta_2(\\mathcal{A})\\ne 0$ if and only if $\\mathcal{A}$ is the Hesse arrangement. We deduce that the multiplicity $e_d(\\mathcal{A})$ of an order $d$ eigenvalue of the monodromy action on the first rational homology of the Milnor fiber is equal to the corresponding Aomoto-Betti number, when $d$ is prime. We give a uniform combinatorial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7137","kind":"arxiv","version":2},"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"}