In Kunz's "Introduction to commutative algebra and algebraic geometry", page 137-139, particular monomial affine curves are described. Here is the link.
In case the curve is not an ideal theoretic complete intersection, how can I prove that the ideal of curve is not generated by 2 elements?
Kunz suggests to consider the ideal $I$ modulo $(X_1^{c_1},X_2^{c_2},X_3^{c_3})$, but I can not develop this argument. Thank you for your help.