the blowup is an isomorphism away from "p", and by working in the affine plane instead of the projective plane, we can give simpler equations for the blowup. after a projective transformation, we may assume that "p" = [0:0:1]. write "x" and "y" for the coordinates on the affine plane "x"≠0. the condition "p" ∈ formula_2 implies that "l" = 0, so we may replace the grassmannian with a p. then the blowup is the variety