Some thoughts on the Jacobian conjecture. III
type: Item
instance of: scholarly article
title: Some thoughts on the Jacobian conjecture. III
zbMATH Open document ID: 1162.14041
published in: Journal of Algebra
publication date: 2008-12-02T00:00:00Z
review text: The paper concerns the two-dimensional Jacobian conjecture for polynomial mappings \((f,g):\mathbb{C}^{2}\rightarrow \mathbb{C}^{2}\). As the author says this paper is only a preparation for proving (in Part IV) a special case of the Jacobian conjecture, called the three minus epsilon characteristic pairs case (it is under an assumption on the characteristic sequence of expansion of \(g\) in terms of \(f\)). The paper is very long (over one hundred pages) and it is written in ``the Abhyankar style''. One can find in it results on the shape of the Newton polygon of non-automorphic Jacobian pair \(f,g\) (Theorem 8.1) and next equivalent conditions to the Jacobian conjecture (Theorem 5.9). For part I, II, cf. J. Algebra 319, No. 2, 493--548 (2008; Zbl 1139.14046); ibid. 319, No. 3, 1154--1248 (2008; Zbl 1139.14047).
reviewed by: Tadeusz Krasiński
Mathematics Subject Classification ID: 14R15
zbMATH DE Number: 5376933
zbMATH Keywords: Jacobian conjecture
zbMATH Keywords: polynomial mapping
zbMATH Keywords: characteristic pairs
zbMATH Keywords: Newton polygon
Wikidata QID: Q122877662
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2008.05.025
OpenAlex ID: W4213361429
cites work: Local analytic geometry
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cites work: Some remarks on the Jacobian question. (Notes by Marius van der Put and William Heinzer, updated by Avinash Sathaye)
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cites work: Some thoughts on the Jacobian conjecture. II
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DOI: 10.1016/J.JALGEBRA.2008.05.025
author: Shreeram S. Abhyankar
description: scientific article; zbMATH DE number 5376933