{"paper":{"title":"Notes on the Kuznetsov component of cubic sevenfolds","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Peize Liu","submitted_at":"2026-07-30T19:15:28Z","abstract_excerpt":"Let $Y$ be a cubic 7-fold. When $Y$ is smooth, its Kuznetsov component is a Calabi-Yau category of dimension 3, and we construct an embedding of the Kuznetsov component into the derived category of Clifford modules over $\\mathbb{P}^4$. When $Y$ is a general cubic 7-fold singular along a line, we construct an explicit weakly crepant categorical resolution of its Kuznetsov component by the derived category of a smooth Calabi-Yau 3-fold, recovering a result of Favero-Kelly. In this construction, we express the resolution functor explicitly as a composition of geometric functors and mutations, and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28784","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/2607.28784/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"}