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

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

2007-04-12

arxiv.org/abs/0704.1561v2

Mathematics

Commutative Algebra

4 pages

Scientific paper

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.

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