On Enriques-Babbage Theorem for singular curves

We propose a version of the Enriques-Babagge Theorem for a singular curve $C$, involving its canonical model $C^{\mathrm{\prime }}$. We provide a partial proof for an arbitrary curve $C$ and complete the proof for unicuspidal monomial curves by describing the generators of the ideal of $C^{\mathrm{\prime }}\subset {\mathbb{P}}^{g-1}$.