Gorenstein toric singularities and convex polytopes
type: Item
instance of: scholarly article
title: Gorenstein toric singularities and convex polytopes
zbMATH Open document ID: 0738.14027
author: Atsushi Noma
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1991-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 52B99
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 4216108
zbMATH Keywords: rational convex polytopes
zbMATH Keywords: normal graded semigroup rings
zbMATH Keywords: toric varieties
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227426
OpenAlex ID: W1964623254
cites work: On graded rings. I
cites work: Toroidal embeddings. I
cites work: Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
cites work: Q4039830
cites work: Hilbert functions of graded algebras
cites work: Some remarks concerning Demazure’s construction of normal graded rings
DOI: 10.2748/TMJ/1178227426
description: scientific article; zbMATH DE number 4216108