Is a projective line $P_{1}$ (brought about by 2 projective points in projective space $P_{n}$ ) a bivariate parametric family?
The aim of the question is to get the concept of a basis in a n-dimensional projective space as a n+1 linearly independent set of projective points and, moreover, the issue of a n+2 point which brings about a "normalization" of those of the former basis-set (that is, the setting of a fixed position of the points within the set, relatively to the quotient space; all this is following a book by Santaló "Projective geometry" (1966)).
Thanks