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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.2337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-11-10T10:43:04Z","cross_cats_sorted":[],"title_canon_sha256":"f23507c4e2c20a19ebbe6debde31a4df30582c8305d25220d3407772e9a3d645","abstract_canon_sha256":"c7a5b5a7a59793234148fe9cb387a47370c4f04d7936a4a84d1155db734500fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:53.309957Z","signature_b64":"4H4mphw5Ibq0FLACZ9HKCBNw+dxC0oO16WItYa6+O9ExyceubeBOKNPyNaZNPzmQ9OTsPt0by8INEQz8Ihz/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a8eb8aef0f00fcdc616d8b6ce8509fb0152c80064100e68b65eee9d69a8db01","last_reissued_at":"2026-05-18T04:19:53.309241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:53.309241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $S_h$. 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