I would like to have a formula for the most general embedding of the Riemann sphere into projective three space, in coordinates. The Veronese maps would be an example of such an embedding, but I'm looking for the most general formula.
I have read the section in Miranda's book "Algebraic Curves and Riemann Surfaces" describing holomorphic embeddings of Riemann surfaces into projective space, where he discusses the concept of very ample line bundle, and how linear systems of a divisor are related to these maps. I have also read the following paper, which mentions a characterization of these maps
https://www.researchgate.net/publication/226072647_The_topology_of_spaces_of_rational_functions
However, the result is mentioned in passing, and I am not sure if it answers the same question (he uses "base point preserving" maps, which may not be the same).
I can probably derive this myself using the techniques in Miranda's book, but I'm wondering if there is a paper/book that does this already, so I don't have to reinvent the wheel.