the standard basis in the exterior space . For any two ordered sequences: of positive integers , the following homogeneous equations are valid, and determine the image of under the Plücker map: where denotes the sequence with the term omitted. When and , the simplest Grassmannian which is not a projective space, the above reduces to a single equation. Denoting the coordinates of by the image of under the Plücker map is defined by the single equation In general, many more equations, as in (), are needed to define the image of the Plücker embedding although these are not, in general, algebraically independent. References Further reading Algebraic geometry Differential geometry