On simplicial toric varieties which are set-theoretic complete intersections
type: Item
instance of: scholarly article
title: On simplicial toric varieties which are set-theoretic complete intersections
zbMATH Open document ID: 0971.14041
author: Margherita Barile
author: Apostolos Thoma
author: Marcel Morales
published in: Journal of Algebra
publication date: 2001-07-04T00:00:00Z
review text: The paper is devoted to the determination of the minimum number of equations needed to define set-theoretically an algebraic variety \(V\) (the arithmetical rank of \(I=I(V)\), denoted by ara\((I))\). If \(h(I)=\text{ara}(I)\) (where \(h(I)\) denotes as usual the height of \(I)\) the ideal \(I\) is called a set-theoretic complete intersection, and when ara\((I)\leq h(I)+1\) it is called almost set-theoretically complete intersection. The authors prove that every simplicial toric affine or projective variety with full parametrization is an almost set-theoretically complete intersection; the same is true for every simplicial toric (affine or projective) variety of codimension two. If the characteristic is positive then every simplicial toric affine or projective variety with full parametrization is actually a set-theoretically complete intersection.
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 1448617
zbMATH Keywords: set-theoretic complete intersection
zbMATH Keywords: arithmetical rank
reviewed by: Giorgio Bolondi
MaRDI profile type: Publication
full work available at URL: jabr.1999.8195
OpenAlex ID: W1971527577
cites work: On the equations defining projective monomial curves
cites work: Complete Intersections in Characteristic p > 0
cites work: Set-Theoretic Complete Intersections
cites work: Equations of monomial varieties in codimension two
cites work: Q3661728
DOI: 10.1006/JABR.1999.8195
description: scientific article; zbMATH DE number 1448617