{"paper":{"title":"Hyperk\\\"ahler fourfolds and Kummer surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atanas Iliev, Grzegorz Kapustka, Kristian Ranestad, Micha{\\l} Kapustka","submitted_at":"2016-03-01T18:56:42Z","abstract_excerpt":"We show that a Hilbert scheme of conics on a Fano fourfold double cover of $\\mathbb{P}^2\\times\\mathbb{P}^2$ ramified along a divisor of bidegree $(2,2)$ admits a $\\mathbb{P}^1$-fibration with base being a hyper-K\\\"{a}hler fourfold. We investigate the geometry of such fourfolds relating them with degenerated EPW cubes, with elements in the Brauer groups of $K3$ surfaces of degree $2$, and with Verra threefolds studied in [Ver04]. These hyper-K\\\"{a}hler fourfolds admit natural involutions and complete the classification of geometric realizations of anti-symplectic involutions on hyper-K\\\"{a}hler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00403","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":""},"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"}