{"paper":{"title":"Stability conditions and moduli spaces on the Kuznetsov component of cubic fivefolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Peize Liu","submitted_at":"2025-09-25T19:24:43Z","abstract_excerpt":"We study the Kuznetsov component of a smooth cubic fivefold. Using a quadric surface fibration, we construct a family of Serre-invariant Bridgeland stability conditions on the Kuznetsov component. For every non-zero numerical class, we prove that the associated Bridgeland moduli space on the Kuznetsov component is non-empty. When the cubic fivefold is general and the numerical class is primitive, the moduli space contains a smooth locus, on which the restriction to a general hyperplane section preserves stability. Consequently, we obtain Lagrangian immersions into hyper-K\\\"ahler varieties aris"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.21454","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/2509.21454/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"}