This online notes, page 10 reads that we can prove the existence of holomorphic embedding into $\mathbb{P}^n$ of a Riemann surface by RR theorem, but I have no idea how to use it. Does anyone have an explanation?
(I guess it's related to the criterion considering certain linear systems of line bundles over the Riemann surface. I have read the results on Hartshorne's book once, but totally unfamiliar with that.)
Moreover, does the method work for the case of higher dimensions?
2026-04-03 21:25:22.1775251522
Embedding of a Riemann surface by Riemann-Roch
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