Universality of Rank 6 Plucker Relations and Grassmann Cone Preserving   Maps
  The Plucker relations define a projective embedding of the Grassmann variety Gr(k,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 from the pth exterior power of n-dimensional space to the 2nd exterior power of 4-dimensional space and pulling back the unique Plucker relation on the latter. We also give a quadratic equation depending on (p+2) parameters having the same properties. 
Alex Kasman, Kathryn Pedings, Amy Reiszl, and Takahiro Shiota