A parachute for the degree of a polynomial in algebraically independent ones

Abstract

We give a simpler proof as well as a generalization of the main result of an article of Shestakov and Umirbaev. This latter article being the first of two that solve a long-standing conjecture about the non-tameness, or "wildness", of Nagata's automorphism. As corollaries we get interesting informations about the leading terms of polynomials forming an automorphism in any dimension and reprove the tameness of automorphisms in dimension two.

arXiv comment4 pages

Cited by in corpus (1)

• Relations between the leading terms of a polynomial automorphism