{"paper":{"title":"The stratification by rank for homogeneous polynomials with border rank 5 which essentially depend on 5 variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Edoardo Ballico","submitted_at":"2017-02-07T07:57:31Z","abstract_excerpt":"We give the stratification by the symmetric tensor rank of all degree $d \\ge 9$ homogeneous polynomials with border rank $5$ and which depend essentially on at least 5 variables, extending previous works (A. Bernardi, A. Gimigliano, M. Id\\`{a}, E. Ballico) on lower border ranks. For the polynomials which depend on at least 5 variables only 5 ranks are possible: $5$, $d+3$, $2d+1$, $3d-1$, $4d-3$, but each of the ranks $3d-1$ and $2d+1$ is achieved in two geometrically different situations. These ranks are uniquely determined by a certain degree 5 zero-dimensional scheme $A$ associated to the p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01914","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"}