... we could also identify An (k) with Ui.We think of the points of Pn (k) \U as being “points at in nity”. The points in Pn (k) \U are those with homogeneous coordinates (x1, . . . , xn, ... = b = 0. In this case we just have the line Z = 0. Asthis line contains no points of U, we think of it as the line at in nity.Proposition 3.10 If p1, p2∈ P2 (k) are distinct points, there ... coordinates (x, 1, 0)} that looks likean affine line and the remaining point with homogeneous coordinates (1, 1, 0)A similar argument to the one above shows that P2(R) looks like the topo-logical...