A new topological proof of the Abhyankar-Moh theorem
type: Item
instance of: scholarly article
title: A new topological proof of the Abhyankar-Moh theorem
zbMATH Open document ID: 1050.14058
author: Henryk Żołądek
published in: Mathematische Zeitschrift
publication date: 2003-09-21T00:00:00Z
review text: The paper presents a new proof of the known Abhyankar-Moh theorem on embeddings of the line in the plane [\textit{S. Abhyankar} and \textit{T. Moh}, J. Reine Angew. Math. 276, 148--166 (1975; Zbl 0332.14004)] that for any injective polynomial mapping \(\Phi :\mathbb C\to \mathbb C^2\) without critical points the image of \(\Phi \) can be transformed to a straight line by a polynomial automorphism of \(\mathbb C^2\). The proof relies on the Poincaré-Hopf theorem on the Euler characteristic of a compact real manifold.
Mathematics Subject Classification ID: 14R10
Mathematics Subject Classification ID: 14E25
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 14J70
zbMATH DE Number: 1983492
zbMATH Keywords: affine space
zbMATH Keywords: polynomial automorphism
zbMATH Keywords: algebraic curve
zbMATH Keywords: rational curve
zbMATH Keywords: embedding
zbMATH Keywords: Abhyankar-Moh theorem
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
full work available at URL: s00209-003-0498-y
OpenAlex ID: W2164147338
DOI: 10.1007/S00209-003-0498-Y
description: scientific article; zbMATH DE number 1983492