Some thoughts on the Jacobian conjecture. III
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).
scientific article; zbMATH DE number 5376933