Minimal generators of the defining ideal of the Rees Algebra associated to monoid parametrizations

We describe a minimal set of generators of the defining ideal of the Rees Algebra associated to a proper parametrization of any monoid hypersurface. In the case of plane curves, we recover a known description for rational parametrizations having a syzygy of minimal degree (\mu=1). We also show that our approach can be applied to parametrizations of rational surfaces having a Hilbert-Burch resolution with \mu_1=\mu_2=1.