{"paper":{"title":"On Invariant Notions of Segre Varieties in Binary Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AG","authors_text":"Boris Odehnal (TUW), Hans Havlicek (TUW), Metod Saniga (ASTRINSTSAV)","submitted_at":"2010-06-23T12:00:10Z","abstract_excerpt":"Invariant notions of a class of Segre varieties $\\Segrem(2)$ of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains $\\Segrem(2)$ and is invariant under its projective stabiliser group $\\Stab{m}{2}$. By embedding PG(2^m - 1, 2) into \\PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under $\\Stab{m}{2}$ as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4492","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"}