{"paper":{"title":"Generalized Zariski cancellation for Brieskorn--Pham varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Buddhadev Hajra, Mohit Upmanyu","submitted_at":"2026-06-25T11:23:24Z","abstract_excerpt":"We establish a generalized Zariski cancellation theorem for Brieskorn--Pham varieties over the field of complex numbers. More precisely, we show that if two complex Brieskorn--Pham varieties become isomorphic after taking a product with an arbitrary separated complex scheme having a smooth point, then they are already isomorphic not merely as complex algebraic varieties but, in fact, as $\\mathbf{C}^*$-varieties. The proof combines our general cancellation theorem for complex algebraic varieties with a unique singularity, whose proof relies on the analytic cancellation theorem of Hauser--M\\\"ull"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.26890","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.26890/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"}