{"paper":{"title":"Veldkamp-Space Aspects of a Sequence of Nested Binary Segre Varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","quant-ph"],"primary_cat":"math.CO","authors_text":"Frederic Holweck, Hans Havlicek, Metod Saniga, Michel Planat, Petr Pracna","submitted_at":"2014-03-26T15:33:57Z","abstract_excerpt":"Let $S_{(N)} \\equiv PG(1,\\,2) \\times PG(1,\\,2) \\times \\cdots \\times PG(1,\\,2)$ be a Segre variety that is $N$-fold direct product of projective lines of size three. Given two geometric hyperplanes $H'$ and $H''$ of $S_{(N)}$, let us call the triple $\\{H', H'', \\overline{H' \\Delta H''}\\}$ the Veldkamp line of $S_{(N)}$. We shall demonstrate, for the sequence $2 \\leq N \\leq 4$, that the properties of geometric hyperplanes of $S_{(N)}$ are fully encoded in the properties of Veldkamp {\\it lines} of $S_{(N-1)}$. Using this property, a complete classification of all types of geometric hyperplanes of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6714","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"}