{"paper":{"title":"A Note on the Strict Transformation of an Effective Cartier Divisor","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yu Zhao","submitted_at":"2023-04-19T07:44:36Z","abstract_excerpt":"Let $Y$ be an effective Cartier divisor of a smooth variety $Z$. Let $X_{i}$, $i\\in \\{1,\\cdots,n\\}$ be a set of pairwise disjoint smooth subvarieties in $Y$ such that their union contains the singular locus of $Y$. In this paper, we give a sufficient condition such that $Bl_{X}Y$ is smooth, where $X$ is the disjoint union of all $X_{i}$. Moreover, we prove that assuming a dimensional condition, there is an admissible subcategory of $D^{b}(Bl_{X}Y)$ which is a weak categorical crepant resolution of $Y$ in the sense of Kuznetsov."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.09475","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/2304.09475/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"}