Corollary 6.11 in Hartshorne:
Every curve is birationally equivalent to a nonsingular projective curve.
And its proof said that any curve with function field $K$ is birationaly equivalent to a set of regular local ring $C_{k}$. But the question is, only the nonsingular point would be birationally equivalent to a regular local ring. What if a curve contains singular points? Does it still biratinally equivalent to a nonsingular projective curve?