{"paper":{"title":"Rouquier dimension of some blow-ups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dmitrii Pirozhkov","submitted_at":"2019-08-22T09:48:20Z","abstract_excerpt":"Rapha\\\"{e}l Rouquier introduced an invariant of triangulated categories which is known as Rouquier dimension. Orlov conjectured that for any smooth quasi-projective variety $X$ the Rouquier dimension of $D^b_{\\mathrm{coh}}(X)$ is equal to $\\mathrm{dim}\\, X$. In this note we show that some blow-ups of projective spaces satisfy Orlov's conjecture. This includes a blow-up of $\\mathbb{P}^2$ in nine arbitrary distinct points, or a blow-up of three distinct points lying on an exceptional divisor of a blow-up of $\\mathbb{P}^3$ in a line. In particular, our method gives an alternative proof of Orlov's"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08283","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/1908.08283/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"}