Constructive invariant theory for tori
type: Item
instance of: scholarly article
title: Constructive invariant theory for tori
zbMATH Open document ID: 0789.14009
author: David Wehlau
publication date: 1994-03-23T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75025
review text: Consider a rational representation of an algebraic torus \(T\) on a vector space \(V\). Suppose that \(\{f_ 1,\dots,f_ p\}\) is a homogeneous minimal generating set for the ring of invariants, \({\mathbf k}[V]^ T\). New upper bounds are derived for the number \(N_{V,T}:=\max \{\deg f_ i\}\). These bounds are expressed in terms of the volume of the convex hull of the weights of \(V\) and other geometric data. Also an algorithm is described for constructing an (essentially unique) partial set of generators \(\{f_ 1,\dots,f_ s\}\) consisting of monomials and such that \({\mathbf k} [V]^ T\) is integral over \(k[f_ 1,\dots,f_ s]\).
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 537210
zbMATH Keywords: torus invariants
zbMATH Keywords: torus representations
zbMATH Keywords: algebraic torus
zbMATH Keywords: ring of invariants
MaRDI profile type: Publication
OpenAlex ID: W2093795107
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DOI: 10.5802/AIF.1364
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 537210