{"paper":{"title":"Gap vectors of real projective varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"Grigoriy Blekherman, Martina Juhnke-Kubitzke, Mauricio Velasco, Sadik Iliman","submitted_at":"2014-07-02T14:31:12Z","abstract_excerpt":"Let $X\\subseteq \\mathbb{P}^m$ be a totally real, non-degenerate, projective variety and let $\\Gamma\\subseteq X(\\mathbb{R})$ be a generic set of points. Let $P$ be the cone of nonnegative quadratic forms on $X$ and let $\\Sigma$ be the cone of sums of squares of linear forms. We examine the dimensions of the faces $P(\\Gamma)$ and $\\Sigma(\\Gamma)$ consisting of forms in $P$ and $\\Sigma$, which vanish on $\\Gamma$. As the cardinality of the set $\\Gamma$ varies in $1,\\dots,\\rm{codim}(X)$, the difference between the dimensions of $P(\\Gamma)$ and $\\Sigma(\\Gamma)$ defines a numerical invariant of $X$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0585","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"}