From a previous question, my understanding is that these are the lines in projective space. In other words, in $\mathbb{P}^n$ we can choose n+1 homogoneous polynomials of degree one for the homogeneous coordinates of the embedding, which will define the most general embedding of the Riemann sphere of degree one.
Is this the unique embedding, and if so what is a good reference where this is proved explicitly (I am mostly looking for a good reference to cite here).