{"paper":{"title":"Brieskorn-Pham singularities via ACM bundles on Geigle-Lenzing projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Jianmin Chen, Shiquan Ruan, Weikang Weng","submitted_at":"2025-01-26T03:12:25Z","abstract_excerpt":"We study the singularity category of the Brieskorn-Pham singularity $R=k[X_1, \\dots, X_4]/(\\sum_{i=1}^{4} X_i^{p_i})$, associated with the Geigle-Lenzing projective space $\\mathbb{X}$ of weight quadruple $(p_1,\\dots, p_4)$, by investigating the stable category $\\underline{\\mathsf{ACM}} \\, \\mathbb{X}$ of arithmetically Cohen-Macaulay bundles on $\\mathbb{X}$.\n  We introduce the notion of $2$-extension bundles on $\\mathbb{X}$, which is a higher dimensional analog of extension bundles on a weighted projective line of Geigle-Lenzing, and then establish a correspondence between $2$-extension bundles"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.15375","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/2501.15375/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"}