Bézoutians and injectivity of polynomial maps
type: Item
instance of: scholarly article
title: Bézoutians and injectivity of polynomial maps
author: Stephen McKean
published in: Journal of Pure and Applied Algebra
publication date: 2023-03-09T00:00:00Z
full work available at URL: https://arxiv.org/abs/2005.09797
review text: In the paper under review, the author uses the multivariate Bézoutian to study polynomial morphisms. He proves that an endomorphism \(f\) is injective on rational points if its multivariate Bézoutian is constant and gives the relations between multivariate Bézoutian and the Jacobians of polynomial endomorphisms. In addition, he also proves an endomorphism \(f\) is injective at a given rational point iff its reduced Bézoutian is constant in the case that the determinate of the Jacobian of \(f\) is a nonzero constant.
reviewed by: Dan Yan
Mathematics Subject Classification ID: 13M10
Mathematics Subject Classification ID: 14R15
zbMATH DE Number: 7661183
MaRDI profile type: Publication
OpenAlex ID: W3193773524
Wikidata QID: Q123281904
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DOI: 10.1016/J.JPAA.2022.107298
description: scientific article; zbMATH DE number 7661183