{"paper":{"title":"Hyperovals of $H(3,q^2)$ when $q$ is even","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Antonio Cossidente, Giuseppe Marino, Oliver H. King","submitted_at":"2012-11-15T16:44:24Z","abstract_excerpt":"For even $q$, a group $G$ isomorphic to $PSL(2,q)$ stabilizes a Baer conic inside a symplectic subquadrangle ${\\cal W}(3,q)$ of ${\\cal H}(3,q^2)$. In this paper the action of $G$ on points and lines of ${\\cal H}(3,q^2)$ is investigated. A construction is given of an infinite family of hyperovals of size $2(q^3-q)$ of ${\\cal H}(3,q^2)$, with each hyperoval having the property that its automorphism group contains $G$. Finally it is shown that the hyperovals constructed are not isomorphic to known hyperovals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3649","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":""},"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"}