{"paper":{"title":"Categorical blow-up formula for Hilbert schemes of points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Naoki Koseki","submitted_at":"2021-10-15T18:49:28Z","abstract_excerpt":"Let $S$ be a smooth projective surface, and $\\hat{S}$ be its blow-up at a point. In this paper, we study the derived category of the Hilbert scheme of points on the blow-up $\\hat{S}$. We obtain a semi-orthogonal decomposition consisting of the derived categories of the Hilbert schemes on the original surface $S$, which recovers the blow-up formula for the Euler characteristics obtained by G\\\"ottsche and Nakajima-Yoshioka. The proof uses the Quot formula, which was conjectured by Jiang and recently proved by Toda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.08315","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/2110.08315/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"}