to give coordinates on the blowup, we can write down equations for the above incidence correspondence. give p homogeneous coordinates ["x":"x":"x"] in which "p" is the point ["p":"p":"p"]. by projective duality, g(1,2) is isomorphic to p, so we may give it homogeneous coordinates ["l":"l":"l"]. a line formula_7 is the set of all ["x":"x":"x"] such that "x""l" + "x""l" + "x""l" = 0. therefore, the blowup can be described as