The Plücker relations are the homogeneous quadratic equations satisfied by the Grassmann coordinates, also called Plücker
coordinates, of the Plücker embedding
of a Grassmannian. If 
denotes the coordinate indexed by a 
-element subset 
, the relations can be written
They generate the homogeneous ideal of the Grassmannian in its Plücker
embedding.
For 
,
the single relation is
The Plücker relations for Grassmannians are distinct from Plücker's equations for
the singularities and dual
curves of plane algebraic curves.
See also
Grassmann Coordinates,
Grassmannian,
Pluecker
Embedding,
Plücker's Equations
Explore with Wolfram|Alpha
References
Harris, J. "Grassmannians and Related Varieties." Lecture 6 in Algebraic
Geometry: A First Course. New York: Springer-Verlag, pp. 63-71, 1992.Shafarevich,
I. R. Basic
Algebraic Geometry, Vol. 1, 2nd ed. Berlin: Springer-Verlag, pp. 42-44,
1994.Referenced on Wolfram|Alpha
Plücker Relations
Cite this as:
Weisstein, Eric W. "Plücker Relations."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PlueckerRelations.html
Subject classifications
