Applications of induced resultants to polynomial maps
type: Item
instance of: scholarly article
title: Applications of induced resultants to polynomial maps
zbMATH Open document ID: 0924.13019
DOI: 10.1007/BF02775035
author: Ronen Peretz
published in: Israel Journal of Mathematics
publication date: 1999-11-07T00:00:00Z
review text: Using the concept of induced resultants for polynomial endomorphisms \(F\) of the affine complex plane \(\mathbb{C}^2\), the author gives simpler proofs of the following facts: Fact 1. If the Jacobian of the map \(F\) is a non-zero constant, then the image of \(F\) misses at most a finite subset of \(\mathbb{C}^2\). Fact 2. If the map \(F\) is invertible, then its inverse is determined by the induced resultants. Fact 3. If the map \(F\) is invertible, then the degree of the map \(F\) is equal to the degree of its inverse.
reviewed by: Arnaldo Garcia
Mathematics Subject Classification ID: 13F20
Mathematics Subject Classification ID: 14H37
zbMATH DE Number: 1286705
zbMATH Keywords: Jacobian conjecture
zbMATH Keywords: induced resultants
zbMATH Keywords: polynomial endomorphisms
MaRDI profile type: Publication
cites work: The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
description: scientific article; zbMATH DE number 1286705