{"paper":{"title":"Relative $m$-ovoids of elliptic quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Cossidente, F. Pavese","submitted_at":"2016-10-03T14:37:04Z","abstract_excerpt":"Let ${\\cal Q}^-(2n+1,q)$ be an elliptic quadric of ${\\rm PG}(2n+1,q)$. A relative $m$-ovoid of ${\\cal Q}^-(2n+1,q)$ (with respect to a parablic section ${\\cal Q} := {\\cal Q}(2n,q) \\subset {\\cal Q}^-(2n+1,q)$) is a subset $\\cal R$ of points of ${\\cal Q}^-(2n+1,q)\\setminus {\\cal Q}$ such that every generator of ${\\cal Q}^-(2n+1,q)$ not contained in $\\cal Q$ meets $\\cal R$ in precisely $m$ points. A relative $m$-ovoid having the same size as its complement (in ${\\cal Q}^-(2n+1,q) \\setminus {\\cal Q}$) is called a relative hemisystem. We show that a nontrivial relative $m$-ovoid of ${\\cal Q}^-(2n+1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00570","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"}