Geodesic
On Spinor Varieties and Their Secants
Symmetry, integrability and geometry: methods and applications, Tome 5 (2009) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type $D_n$, cubic equations exist if and only if $n\ge9$. In general the ideal has generators in degrees at least three and four. Finally we observe that the other Freudenthal varieties exhibit strikingly similar behaviors.
Keywords: spinor variety; spin representation; secant variety; Freudenthal variety. 
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     author = {Laurent Manivel},
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Laurent Manivel. On Spinor Varieties and Their Secants. Symmetry, integrability and geometry: methods and applications, Tome 5 (2009). http://geodesic.mathdoc.fr/item/SIGMA_2009_5_a77/

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