L. G. Makar-Limanov, “On the Newton polyhedron of a Jacobian pair”, Izv. RAN. Ser. Mat., 2021, Volume 85, Issue 3,Pages <nobr>127

This article is cited in 1 paper

On the Newton polyhedron of a Jacobian pair

L. G. Makar-Limanov^ab

^a Wayne State University, Department of Mathematics, Detroit, MI, USA
^b Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, Israel

Abstract: We introduce and describe the Newton polyhedron related to a “minimal” counterexample to the Jacobian conjecture. This description allows us to obtain a sharper estimate for the geometric degree of the polynomial mapping given by a Jacobian pair and to give a new proof in the case of the Abhyankar's two characteristic pairs.

Keywords: Jacobian conjecture, Newton polytopes.

UDC: 512.552.16+512.622+512.714+514.172.45

MSC: Primary 14R15, 12E05; Secondary 12E12

Received: 04.06.2020
Revised: 06.07.2020

DOI: 10.4213/im9067