An embedding theorem for smooth projective toric varieties
type: Item
instance of: scholarly article
title: An embedding theorem for smooth projective toric varieties
zbMATH Open document ID: 0672.14005
DOI: 10.1007/BF01830947
published in: Aequationes Mathematicae
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137267
review text: It is known that a compact projective toric variety \(X_{\Delta}\) can be constructed by means of a convex polytope \(\Delta\) obtained as intersection of translated cones. On the other hand a general embedding of \(X_{\Delta}\) in a projective space \({\mathbb{P}}^ k\) is not a complete intersection. The author proves that any n-dimensional smooth complete projective toric variety \(X_{\Delta}\) can be embedded into a projective space \({\mathbb{P}}^ k\) as zero locus of finitely many homogeneous monomial equations. Moreover he finds out, both for k and for the number q of such equations, a bound related to the number of vertices of \(\Delta\).
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 14M10
zbMATH DE Number: 4099459
zbMATH Keywords: embedding smooth toric varieties
zbMATH Keywords: complete intersection
zbMATH Keywords: zero locus of finitely many homogeneous monomial equations
author: Günter Ewald
reviewed by: Luciana Picco Botta
MaRDI profile type: Publication
cites work: Q5547252
cites work: Über eine Klasse von einfach-zusammenhängenden komplexen Mannigfaltigkeiten. (On a class of simply connected complex manifolds)
cites work: Toroidal embeddings. I
cites work: A classification of toric varieties with few generators
cites work: Affine torus embeddings which are complete intersections
cites work: Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
OpenAlex ID: W1985279884
description: scientific article; zbMATH DE number 4099459