A remark on the two-dimensional Jacobian conjecture
type: Item
instance of: scholarly article
title: A remark on the two-dimensional Jacobian conjecture
zbMATH Open document ID: 0810.13019
DOI: 10.1016/0022-4049(94)90083-3
published in: Journal of Pure and Applied Algebra
publication date: 1994-11-03T00:00:00Z
review text: Let \(k\) be an algebraically closed field of characteristic zero. Let \(F = (f,g) : k^ 2 \to k^ 2\) be a polynomial map. It is shown that if \(\text{det} JF \in k^*\) and there exist three concurrent lines such that the restriction of \(F\) to each of these lines is injective, then \(F\) is invertible. A corollary is that if \(F\) is of the form \(F=X+H\) with \(H\) homogeneous of degree \(\geq 2\) and \(\text{det} JF \in k^*\), then \(F\) is invertible.
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 681829
zbMATH Keywords: Jacobian conjecture
zbMATH Keywords: polynomial map
Wikidata QID: Q123289963
author: Arno van den Essen
author: Halszka Tutaj-Gasińska
reviewed by: David E. Rush
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90083-3
OpenAlex ID: W2080713757
cites work: Lectures on expansion techniques in algebraic geometry. With notes by Balwant Singh
cites work: Q4097032
cites work: Eulerian systems of partial differential equations and the Jacobian conjecture
cites work: Q5622339
cites work: On the jacobian equation J(f, g) = 0 for Polynomials in k[x, y]
description: scientific article; zbMATH DE number 681829