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arXiv · 0904.0565

On spinor varieties and their secants

Laurent Manivel
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Abstract

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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Laurent Manivel. 2009-07-24. On spinor varieties and their secants. https://doi.org/10.3842/sigma.2009.078

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