{"paper":{"title":"Categorical resolutions of cuspidal singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"C\\'eline Fietz","submitted_at":"2024-11-28T21:15:05Z","abstract_excerpt":"Let $X$ be a projective variety with an isolated $A_2$ singularity. We study its bounded derived category and prove that there exists a crepant categorical resolution $\\pi_*\\colon \\widetilde{\\mathcal{D}} \\to D^b(X)$, which is a Verdier localization. More importantly, we give an explicit description of a generating set for its kernel. In the case of an even dimensional variety with a single $A_2$ singularity, we prove that this generating set is given by two $2$-spherical objects. If $X$ is a cubic fourfold with an isolated $A_2$ singularity, we show that this resolution restricts to a crepant "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.19380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.19380/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"}