{"paper":{"title":"Bernstein-Sato Varieties and Annihilation of Powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.CV"],"primary_cat":"math.AG","authors_text":"Daniel Bath","submitted_at":"2019-07-11T15:22:30Z","abstract_excerpt":"Given a complex germ $f$ near the point $\\mathfrak{x}$ of the complex manifold $X$, equipped with a factorization $f = f_{1} \\cdots f_{r}$, we consider the $\\mathscr{D}_{X,\\mathfrak{x}}[s_{1}, \\dots, s_{r}]$-module generated by $ F^{S} := f_{1}^{s_{1}} \\cdots f_{r}^{s_{r}}$. We show for a large class of germs that the annihilator of $F^{S}$ is generated by derivations and this property does not depend on the chosen factorization of $f$.\n  We further study the relationship between the Bernstein-Sato variety attached to $F$ and the cohomology support loci of $f$, via the $\\mathscr{D}_{X,\\mathfra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05301","kind":"arxiv","version":4},"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/1907.05301/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"}