Multidegrees of Tame automorphisms with one prime number

2012/04/04 by Jiantao Li, Li, Jiantao, Xiankun Du +1 · 1 citation
Mathematics · #14R10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1204.0930

openalex publication_date 2012/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let 3≤ d₁≤ d₂≤ d₃ be integers. We show the following results: (1) If d₂ is a prime number and (d₁)/(gcd(d₁,d₃))≠2, then (d₁,d₂,d₃) is a multidegree of a tame automorphism if and only if d₁=d₂ or d₃∈ d₁ℕ+d₂ℕ; (2) If d₃ is a prime number and gcd(d₁,d₂)=1, then (d₁,d₂,d₃) is a multidegree of a tame automorphism if and only if d₃∈ d₁ℕ+d₂ℕ. We also relate this investigation with a conjecture of Drensky and Yu, which concerns with the lower bound of the degree of the Poisson bracket of two polynomials, and we give a counter-example to this conjecture.

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• Weighted multidegrees of polynomial automorphisms over a domain

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