In this work, we describe a prenormal form for the generators of the semigroup of a toric variety $X \subset \mathbb{ C}^p$ with isolated singularity at the origin and smooth normalization. A complete description of the semigroup is given when $X$ is a variety of dimension $n$ in $\mathbb{ C}^{ 2n}$. Moreover, for toric surfaces in $\mathbb{ C}^4$, we provide a set of generators of the ideal $I$ defining $X$.
Categories: math.AG