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

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
@article{BUMI_2011_9_4_2_a2,
     author = {Angelini, Elena},
     title = {Higher {Secants} of {Spinor} {Varieties}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {213--235},
     publisher = {mathdoc},
     volume = {Ser. 9, 4},
     number = {2},
     year = {2011},
     zbl = {1253.15032},
     mrnumber = {2840603},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2011_9_4_2_a2/}
}
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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/