{"paper":{"title":"On the homeomophism type of smooth projective fourfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Keiji Oguiso, Thomas Peternell","submitted_at":"2017-07-18T14:55:04Z","abstract_excerpt":"In this paper we study smooth complex projective $4$-folds which are topologically equivalent. First we show that Fano fourfolds are never oriented homeomorphic to Ricci-flat projective fourfolds and that Calabi-Yau manifolds and hyperk\\\"ahler manifolds in dimension $\\ge 4$ are never oriented homeomorphic. Finally, we give a coarse classification of smooth projective fourfolds which are oriented homeomorphic to a hyperk\\\"ahler fourfold which is deformation equivalent to the Hilbert scheme $S^{[2]}$ of two points of a projective K3 surface $S.$ We also present an explicit example of a smooth pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05657","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}