{"paper":{"title":"Combinatorially Determined Zeroes of Bernstein--Sato Ideals for Tame and Free Arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Bath","submitted_at":"2019-09-02T05:02:33Z","abstract_excerpt":"For a central, not necessarily reduced, hyperplane arrangement $f$ equipped with any factorization $f = f_{1} \\cdots f_{r}$ and for $f^{\\prime}$ dividing $f$, we consider a more general type of Bernstein--Sato ideal consisting of the polynomials $B(S) \\in \\mathbb{C}[s_{1}, \\dots, s_{r}]$ satisfying the functional equation $B(S) f^{\\prime} f_{1}^{s_{1}} \\cdots f_{r}^{s_{r}} \\in \\text{A}_{n}(\\mathbb{C})[s_{1}, \\dots, s_{r}] f_{1}^{s_{1} + 1} \\cdots f_{r}^{s_{r} + 1}.$\n  Generalizing techniques due to Maisonobe, we compute the zero locus of the standard Bernstein--Sato ideal in the sense of Budur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.00547","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.00547/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"}