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.References
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Additional Information
- Alex Kasman
- Affiliation: Department of Mathematics, College of Charleston, 66 George Street, Charleston, South Carolina 29424
- MR Author ID: 366818
- 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
- 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
- © Copyright 2007 American Mathematical Society
- 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
- MathSciNet review: 2350391