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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 078, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.078 (Mi sigma423) 		 
This article is cited in 16 scientific papers (total in 16 papers)

On Spinor Varieties and Their Secants

Laurent Manivel

Institut Fourier, Université de Grenoble I et CNRS, BP 74, 38402 Saint-Martin d'Hères, France
Full-text PDF (327 kB) Citations (16)
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DOI: https://doi.org/10.3842/SIGMA.2009.078
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 $n\ge9$. 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.
Keywords: spinor variety; spin representation; secant variety; Freudenthal variety.
Received: April 3, 2009; in final form July 21, 2009; Published online July 24, 2009
Bibliographic databases:
Document Type: Article
MSC: 14M17; 15A66; 14L35; 14N15
Language: English
Citation: Laurent Manivel, “On Spinor Varieties and Their Secants”, SIGMA, 5 (2009), 078, 22 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 16 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
     
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