{"paper":{"title":"On Hyperk\\\"ahler manifolds of K3$^{[n]}$-type with large Picard number","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Yulieth Prieto-Monta\\~nez","submitted_at":"2024-08-29T15:18:44Z","abstract_excerpt":"Inspired by well-known examples of hyperk\\\"ahler manifolds, we show that any hyperk\\\"ahler manifold $X$ of K3$^{[n]}$-type with Picard number $\\rho(X) \\geq 4$ is always isomorphic to a moduli space of twisted stable sheaves on a K3 surface. Additionally, we provide explicit descriptions of hyperk\\\"ahler manifolds of K3$^{[n]}$-type with Picard ranks below this crucial value (e.g., $\\rho(X)=3$) that are not birational to such moduli spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.16610","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/2408.16610/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"}