{"paper":{"title":"Motivic zeta functions of hyperplane arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jeremy Usatine, Max Kutler","submitted_at":"2018-10-26T23:24:25Z","abstract_excerpt":"For each central essential hyperplane arrangement $\\mathcal{A}$ over an algebraically closed field, let $Z_\\mathcal{A}^{\\hat\\mu}(T)$ denote the Denef-Loeser motivic zeta function of $\\mathcal{A}$. We prove a formula expressing $Z_\\mathcal{A}^{\\hat\\mu}(T)$ in terms of the Milnor fibers of related hyperplane arrangements. We use this formula to show that the map taking each complex arrangement $\\mathcal{A}$ to the Hodge-Deligne specialization of $Z_{\\mathcal{A}}^{\\hat\\mu}(T)$ is locally constant on the realization space of any loop-free matroid. We also prove a combinatorial formula expressing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11552","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"}