Universality of Rank 6 Plücker relations and Grassmann cone preserving maps

Kasman, Alex; Pedings, Kathryn; Reiszl, Amy; Shiota, Takahiro

doi:10.1090/S0002-9939-07-09122-8

Universality of Rank 6 Plücker relations and Grassmann cone preserving maps
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by Alex Kasman, Kathryn Pedings, Amy Reiszl and Takahiro Shiota PDF

Proc. Amer. Math. Soc. 136 (2008), 77-87 Request permission

Abstract:

The Plücker relations define a projective embedding of the Grassmann variety $Gr(p,n)$. We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. This is achieved by constructing a certain finite set of linear maps $\bigwedge ^pk^n\to \bigwedge ^2k^4$, and pulling back the unique Plücker relation on $\bigwedge ^2k^4$. We also give a quadratic equation depending on $(p+2)$ parameters having the same properties.

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