Geodesic
Higher Secants of Spinor Varieties
Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 213-235.

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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 an algorithm which computes the complex dimension of $\sigma_{k}(S_{h})$. Then, by using an inductive argument, we get our main result: $\sigma_{k}(S_{h})$ 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. 
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Angelini, Elena. Higher Secants of Spinor Varieties. Bollettino della Unione matematica italiana, Série 9, Tome 4 (2011) no. 2, pp. 213-235. http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a2/

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