{"paper":{"title":"On the variety parametrizing completely decomposable polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"A. Bernardi, E. Arrondo","submitted_at":"2009-03-16T14:26:33Z","abstract_excerpt":"The purpose of this paper is to relate the variety parameterizing completely decomposable homogeneous polynomials of degree $d$ in $n+1$ variables on an algebraically closed field, called $\\Split_{d}(\\PP n)$, with the Grassmannian of $n-1$ dimensional projective subspaces of $\\PP {n+d-1}$. We compute the dimension of some secant varieties to $\\Split_{d}(\\PP n)$ and find a counterexample to a conjecture that wanted its dimension related to the one of the secant variety to $\\GG (n-1, n+d-1)$. Moreover by using an invariant embedding of the Veronse variety into the Pl\\\"ucker space, then we are ab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.2757","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"}