A normal \((0,1)\)-polytope none of whose regular triangulations is unimodular
type: Item
instance of: scholarly article
title: A normal \((0,1)\)-polytope none of whose regular triangulations is unimodular
zbMATH Open document ID: 0927.52018
DOI: 10.1007/PL00009415
author: Hidefumi Ohsugi
author: Takayuki Hibi
published in: Discrete \& Computational Geometry
publication date: 1999-12-14T00:00:00Z
review text: The authors study integral convex polytopes \({\mathcal P}\subset \mathbb{R}^N\). Such a polytope \({\mathcal P}\) is called normal if the subalgebra of \(K[t_1,t^{-1}_1,\dots, t_N, t^{-1}_N, s]\) which is generated by all monomials \(t^{\alpha_1}_1\cdots t^{\alpha_N}_N,s\) with \((\alpha_1,\dots,\alpha_N)\in {\mathcal P}\cap \mathbb{Z}^N\) is normal, i.e. integrally closed in its quotient field. The property that a polytope \({\mathcal P}\) possesses a unimodular regular covering is known to imply that \({\mathcal P}\) is normal. The authors show that the converse is false by constructing a normal \((0,1)\)-polytope none of whose regular triangulation is unimodular. The proof relies on earlier work by B. Sturmfels and the authors.
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 1271053
zbMATH Keywords: normal polytope
zbMATH Keywords: regular triangulation
zbMATH Keywords: unimodular
zbMATH Keywords: edge polytope
reviewed by: Charles Leytem
MaRDI profile type: Publication
full work available at URL: pl00009415
OpenAlex ID: W2036271623
description: scientific article; zbMATH DE number 1271053