I am looking for a book which shows that the function field of an affine plane curve has transcendence degree 1.
Sincerely, Hypertrooper
2026-03-27 07:18:53.1774595933
The function field of an affine plane curve has transcendence degree one
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By Noether normalization lemma the question reduces to $X = \Bbb A^1$ and in this case the answer is clear.