{"paper":{"title":"EPW sextics and Hilbert squares of K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Atanas Iliev, Carlo Madonna","submitted_at":"2013-08-13T09:36:02Z","abstract_excerpt":"We prove that the Hilbert square $S^{[2]}$ of a very general primitively polarized K3 surface S of degree $d(n) = 2(4n^2 + 8n + 5)$, $n \\geq 1$ is birational to a double Eisenbud-Popescu-Walter sextic. Our result implies a positive answers, in the case when $r$ is even, to a conjecture of O'Grady: On the Hilbert square of a very general K3 surface of genus $r^2 + 2$, $r \\geq 1$ there is an antisymplectic involution. We explicitly give this involution on $S^{[2]}$ in term of the corresponding EPW polarization on it."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2800","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"}