Let $X$ be a reduced projective scheme of pure dimension 1 over a field $k$.
What is the minimal number $N$ such that there is a closed immersion $X \to \mathbb{P}_k^N$?
For smooth $X$ this should be $N=3$ and for singular curves, this should definitely depend on the singularities (because of the tangent space that have higher dimension).
Where do I find such a result? Any hints and references are welcome, thank you!