{"paper":{"title":"Partial stratification of secant varieties of Veronese varieties via curvilinear subschemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Bernardi, E. Ballico","submitted_at":"2010-10-18T10:24:02Z","abstract_excerpt":"We give a partial \"quasi-stratification\" of the secant varieties of the order $d$ Veronese variety $X_{m,d}$ of $\\mathbb {P}^m$. It covers the set $\\sigma_t(X_{m,d})^{\\dagger}$ of all points lying on the linear span of curvilinear subschemes of $X_{m,d}$, but two \"quasi-strata\" may overlap. For low border rank two different \"quasi-strata\" are disjoint and we compute the symmetric rank of their elements. Our tool is the Hilbert schemes of curvilinear subschemes of Veronese varieties. To get a stratification we attach to each $P\\in \\sigma_t(X_{m,d})^{\\dagger}$ the minimal label of a quasi-stratu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.3546","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"}