“…For s > 4, the ideal of s points of P 1 × P 1 is the ideal of s lines in P 3 , but the lines are never general, even if the points are.) Moving to P 1 × P 1 makes available to us the vast array of work done on products of projective spaces and surfaces in general, and on P 1 × P 1 in particular; see, for example [12,14,18,25,28,30].…”