On spinor varieties and their secants

Details On spinor varieties and their secants On spinor varieties and their secants

2009-04-03

arxiv.org/abs/0904.0565v2

Symmetry, Integrability and Geometry: Methods and Applications 5 (2009) 078

Mathematics

Algebraic Geometry

Scientific paper

10.3842/SIGMA.2009.078

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.

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