Toric varieties with isolated singularity and smooth normalization

Abstract

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 $X$.