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

2007/04/12 by Stéphane Vénéreau, Vénéreau, Stéphane
Mathematics · #13F20 #13P10 #14R10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13F20 #msc:13P10 #msc:14R10

paper · pdf · doi:10.48550/arxiv.0704.1561

4 pages

arxiv created 2007/05/07 · arxiv updated 2009/12/01

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.

Related

• Gradings allowing wild automorphisms
• Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism
• On the Karaś type theorems for the multidegrees of polynomial automorphisms
• Wildness of polynomial automorphisms in three variables
• On polynomial automorphisms of Nagata type