Minimal closed embedding of singular projective curve into some projective space

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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!