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Proceedings of the American Mathematical Society

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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
Published electronically: October 11, 2007
MathSciNet review: 2350391
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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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Additional Information

Alex Kasman
Affiliation: Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424
Email: kasman@cofc.edu

Kathryn Pedings
Affiliation: Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424
Email: kepedings@edisto.cofc.edu

Amy Reiszl
Affiliation: Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424
Email: amreiszl@edisto.cofc.edu

Takahiro Shiota
Affiliation: Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

DOI: https://doi.org/10.1090/S0002-9939-07-09122-8
Received by editor(s): September 30, 2005
Received by editor(s) in revised form: January 31, 2007
Published electronically: October 11, 2007
Communicated by: Michael Stillman
Article copyright: © Copyright 2007 American Mathematical Society