thinking of the real g2 point grassmanian as the projective light cone in the imaginary split octonions, the 2d schubert variety in it at a basepoint k is carved out by the equation "x*k=0". can we as simply carve out the 4d schubert variety?

i guess that this raises some interesting questions about the "algebraic geometry as a form of logic" program and how the algebra of resultants (used in calculating some concept of "image of an algebraic-geometric map") relates to lawvere's analysis of existential quantification as an adjoint to substitution. thus we want the equational hull of "there exists y such that x*y=0 and y*k=0", or something like that.