{"paper":{"title":"Higher secants of spinor varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Elena Angelini","submitted_at":"2010-11-10T10:43:04Z","abstract_excerpt":"Let $S_h$ be the even pure spinors variety of a complex vector space $V$ of even dimension $2h$ endowed with a non degenerate quadratic form $Q$ and let $\\sigma_k(S_h) $ be the $k$-secant variety of $S_h$. We decribe a probabilistic algorithm which computes the complex dimension of $\\sigma_k(S_h) $. Then, by using an inductive argument, we get our main result: $\\sigma_3(S_h) $ has the expected dimension except when $h\\in \\{7,8\\} $. Also we provide theoretical arguments which prove that $S_7$ has a defective 3-secant variety and $S_8$ has defective 3-secant and 4-secant varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2337","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"}