{"paper":{"title":"On line covers of finite projective and polar spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Cossidente, F. Pavese","submitted_at":"2018-06-30T11:39:04Z","abstract_excerpt":"An $m$-$cover$ of lines of a finite projective space ${\\rm PG}(r,q)$ (of a finite polar space $\\cal P$) is a set of lines $\\cal L$ of ${\\rm PG}(r,q)$ (of $\\cal P$) such that every point of ${\\rm PG}(r,q)$ (of $\\cal P$) contains $m$ lines of $\\cal L$, for some $m$. Embed ${\\rm PG}(r,q)$ in ${\\rm PG}(r,q^2)$. Let $\\bar{\\cal L}$ denote the set of points of ${\\rm PG}(r,q^2)$ lying on the extended lines of $\\cal L$.\n  An $m$-cover $\\cal L$ of ${\\rm PG}(r,q)$ is an $(r-2)$-dual $m$-cover if there are two possibilities for the number of lines of $\\cal L$ contained in an $(r-2)$-space of ${\\rm PG}(r,q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00156","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"}