In Hartshorne Chapter IV:
Corollary 3.6. Any curve can be embedded in $\mathbb{P}^3$.
What is the precise definition of embedding here.
2026-03-26 13:49:43.1774532983
Embedding a curve in projective space
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The author means a closed embedding, also called a closed immersion. So the precise statement is: given a curve $X$, there is a closed immersion $X \to \mathbb{P}^3$. (This is clear from the two propositions immediately preceding the corollary.)