{"paper":{"title":"A geometric invariant of $6$-dimensional subspaces of $4\\times 4$ matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Alex Chirvasitu, Michaela Vancliff, S. Paul Smith","submitted_at":"2015-12-12T19:39:12Z","abstract_excerpt":"Let $k$ be an algebraically closed field and ${\\sf G}(2,k^4)$ the Grassmannian of 2-planes in $k^4$. We associate to each 6-dimensional subspace $R$ of the space of 4x4 matrices over $k$ a closed subscheme ${\\bf X}_R \\subseteq {\\sf G}(2,k^4)$. We show that each irreducible component of ${\\bf X}_R$ has dimension at least one and when ${\\rm dim}({\\bf X}_R)=1$, then ${\\rm deg}({\\bf X}_R)=20$ where degree is computed with respect to the ambient ${\\mathbb P}^5$ under the Pl\\\"ucker embedding ${\\sf G}(2,k^4) \\to {\\mathbb P}^5$. We give two examples involving elliptic curves: in one case ${\\bf X}_R$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03954","kind":"arxiv","version":3},"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"}