On the hull resolution of an affine monomial curve

We characterize the hull resolution of a monomial curve in three-dimensional affine space, and we compare this resolution with the minimal one. Concretely, we give a necessary and sufficient condition for the minimality of the hull resolution of a monomial curve in three-dimensional affine space in terms of the associated semigroup. We also get a lower bound for the Betti numbers of the minimal free resolution of a generic monomial curve, in four- and five-dimensional affine space.