Higher secants of spinor varieties

Abstract

Let $S_h$ be the even pure spinors variety of a complex vector space $V$ of even dimension $2h$ endowed with a non degenerate quadratic form $Q$ and let ${\sigma }_k(S_h)$ be the $k$-secant variety of $S_h$. We decribe a probabilistic algorithm which computes the complex dimension of ${\sigma }_k(S_h)$. Then, by using an inductive argument, we get our main result: ${\sigma }_3(S_h)$ has the expected dimension except when $h\in \{7,8\}$. Also we provide theoretical arguments which prove that $S_7$ has a defective 3-secant variety and $S_8$ has defective 3-secant and 4-secant varieties.

23 pages

References in corpus (2)

• On spinor varieties and their secants
• Secant Varieties of (P ^1) X .... X (P ^1) (n-times) are NOT Defective for n \geq 5