I don't know of a good writeup, but y^3 - y = 0, or alternatively x^3 - x = 0, among other polynomials, is what you want. In "ordinary" algebra, typically we c

I don't know of a good writeup, but y^3 - y = 0, or alternatively x^3 - x = 0, among other polynomials, is what you want. In "ordinary" algebra, typically we consider polynomials of one variable, which we write f(x). The graph of the polynomial represents the set of solutions to y = f(x), or alternatively y - f(x) = 0. In algebraic geometry, the solution set to y - f(x) = 0 is indeed a plane curve, but we think of y - f(x) as a special case of a polynomial in the two variables x and y. All such polynomials (except constant polynomials) also define plane curves. This is the concept that generalizes. In particular: y^3 - y = 0 and x^3 - x = 0 are both plane curves, they are both polynomials in x and y (i.e. we can think of y^3 - y = 0 as a polynomial in not only y but also x, even though x doesn't appear), and the intersection of these two curves is the set of nine points in question. Hope this helps.