{"paper":{"title":"F-purity of hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Daniel J. Hern\\'andez","submitted_at":"2011-12-12T02:34:07Z","abstract_excerpt":"In this note, we study F-purity of pairs, and show (as is the case with log canonicity) that F-purity is preserved at the F-pure threshold. We also characterize when F-purity is equivalent to sharp F-purity, an alternate notion of purity for pairs introduced in [Sch08]. These results on purity at the threshold generalize results appearing in [Har06, Sch08], and were expected to hold by many experts in the field. We conclude by extending results in [BMS09] on the set of all F-pure thresholds to the most general setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2424","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"}