On Spinor Varieties and Their Secants - Manivel, L. (Symmetry, Integrability and Geometry: Methods and Applications, 2009)
We study the secant variety of the spinor variety, focusing on its equations of degree three and four. We show that in type Dn, cubic equations exist if and only if n ≥ 9. 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.