Gorenstein toric singularities and convex polytopes
We prove that every projective toric variety is isomorphic to the Proj of a normal, Gorenstein, graded ring with a natural semigroup structure, based on a criterion of \textit{K. Watanabe} [Nagoya Math. J. 83, 203-211 (1981; Zbl 0518.13003)]. To this end, we discuss a relationship among rational convex polytopes, normal graded semigroup rings, and projective toric varieties with an ample \(\mathbb{Q}\)-divisor stable under the torus action, according to \textit{T. Oda} [Convex bodies and algebraic geometry. An introduction to the theory of toric varieties. (1988; Zbl 0628.52002)].
scientific article; zbMATH DE number 4216108