{"paper":{"title":"A family of $m$-ovoids of parabolic quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Koji Momihara, Qing Xiang, Tao Feng","submitted_at":"2015-09-02T02:59:53Z","abstract_excerpt":"We construct a family of $\\frac{(q-1)}{2}$-ovoids of $Q(4,q)$, the parabolic quadric of $\\textup{PG}(4,q)$, for $q\\equiv 3\\pmod 4$. The existence of $\\frac{(q-1)}{2}$-ovoids of $Q(4,q)$ was only known for $q=3, 7,$ or $11$. Our construction provides the first infinite family of $\\frac{(q-1)}{2}$-ovoids of $Q(4,q)$.Along the way, we also give a construction of $\\frac{q+1}{2}$-ovoids in $Q(4,q)$ for $q\\equiv 1\\pmod 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00550","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"}