{"paper":{"title":"Degeneration of pole order spectral sequences for hyperplane arrangements of 4 variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Morihiko Saito","submitted_at":"2019-02-11T12:10:09Z","abstract_excerpt":"For essential reduced hyperplane arrangements of 4 variables, we show that the pole order spectral sequence degenerates almost at $E_2$, and completely at $E_3$, generalizing the 3 variable case where the complete $E_2$-degeneration is known. These degenerations are useful to determine the roots of Bernstein-Sato polynomials supported at the origin. For the proof we improve an estimate of the Castelnuovo-Mumford regularity of logarithmic vector fields which was studied by H. Derksen and J. Sidman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03838","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"}