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

Authors: Alex Kasman, Kathryn Pedings, Amy Reiszl and Takahiro Shiota
Journal: Proc. Amer. Math. Soc. 136 (2008), 77-87
MSC (2000): Primary 14M15, 15A75
DOI: https://doi.org/10.1090/S0002-9939-07-09122-8
Published electronically: October 11, 2007
MathSciNet review: 2350391
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Abstract: The Plücker relations define a projective embedding of the Grassmann variety . 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 parameters having the same properties.

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