On spinor varieties and their secants

Laurent Manivel (1)

1 IF - Institut Fourier

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 $n\ge 9$. 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.

Mots clés: spinor variety; spin representation; secant variety; Freudenthal variety

Domaines: Géométrie algébrique [math.AG]; Théorie des représentations [math.RT]

Laurent Manivel. On spinor varieties and their secants. Symmetry, Integrability and Geometry : Methods and Applications, 2009, 5, pp.078. ⟨10.3842/SIGMA.2009.078⟩. ⟨hal-00373106v2⟩