{"paper":{"title":"k-nets embedded in a projective plane over a field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"G. Korchmaros, G.P. Nagy, N. Pace","submitted_at":"2013-06-24T20:56:27Z","abstract_excerpt":"We investigate $k$-nets with $k\\geq 4$ embedded in the projective plane $PG(2,\\mathbb{K})$ defined over a field $\\mathbb{K}$; they are line configurations in $PG(2,\\mathbb{K})$ consisting of $k$ pairwise disjoint line-sets, called components, such that any two lines from distinct families are concurrent with exactly one line from each component. The size of each component of a $k$-net is the same, the order of the $k$-net. If $\\mathbb{K}$ has zero characteristic, no embedded $k$-net for $k\\geq 5$ exists; see [1,2]. Here we prove that this holds true in positive characteristic $p$ as long as $p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5779","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"}