{"paper":{"title":"The hyper-Kummer construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Lie Fu, Salvatore Floccari","submitted_at":"2026-07-08T15:21:25Z","abstract_excerpt":"The hyper-Kummer construction, discovered by the first-named author, associates a hyper-K\\\"ahler manifold of $\\mathrm{K}3^{[3]}$-type with any hyper-K\\\"ahler sixfold of generalized Kummer type. We regard this construction as a higher-dimensional analog of the classical Kummer construction of K3 surfaces from abelian surfaces. In this spirit, we prove several results which parallel those known for the classical Kummer construction: we characterize the hyper-Kummer $\\mathrm{K}3^{[3]}$-manifolds up to birational equivalence in terms of their Hodge lattices, and establish a McKay correspondence fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.07528","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/2607.07528/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"}