On Spinor Varieties and Their Secants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• ISSN: 1815-0659
• Main Author: Manivel, L.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149143
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: On Spinor Varieties and Their Secants / L. Manivel // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 15 назв. — англ.

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...