# Multidegrees of tame automorphisms of C^n

@article{Karas2011MultidegreesOT,
title={Multidegrees of tame automorphisms of C^n},
author={Marek Kara's},
journal={arXiv: Algebraic Geometry},
year={2011}
}
• Marek Kara's
• Published 2011
• Mathematics
• arXiv: Algebraic Geometry
Let F=(F_1,...,F_n):C^n --> C^n be a polynomial mapping. By the multidegree of the mapping F we mean mdeg F=(deg F_1,...,deg F_n), an element of N^n. The aim of this paper is to study the following problem (especially for n=3): for which sequence (d_1,...,d_n) in N^n there is a tame automorphism F of C^n such that mdeg F=(d_1,...,d_n). In other words we investigate the set mdeg(Tame(C^n)), where Tame(C^n) denotes the group of tame automorphisms of C^n and mdeg denotes the mapping from the set… Expand
7 Citations
Multidegrees of tame automorphisms with one prime number
• Mathematics
• 2012
Let $3\leq d_1\leq d_2\leq d_3$ be integers. We show the following results: (1) If $d_2$ is a prime number and $\frac{d_1}{\gcd(d_1,d_3)}\neq2$, then $(d_1,d_2,d_3)$ is a multidegree of a tameExpand
Dependence of Homogeneous Components of Polynomials with Small Degree of Poisson Bracket
• Mathematics
• 2021
Let F,G ∈ C[x1, . . . , xn] be two polynomials in n variables x1, . . . , xn over the complex numbers field C. In this paper, we prove that if the degree of the Poisson bracket [F,G] is small enoughExpand
On the Kara\'s type theorems for the multidegrees of polynomial automorphisms
To solve Nagata's conjecture, Shestakov-Umirbaev constructed a theory for deciding wildness of polynomial automorphisms in three variables. Recently, Kara\'s and others study multidegrees ofExpand
Separability of wild automorphisms of a polynomial ring
• Mathematics
• 2013
For a large class (including the Nagata automorphism) of wild automorphisms F of k[x, y, z] (where k is a field of characteristic zero), we prove that we can find a weight w such that there exists noExpand
The Jacobian Conjecture, Together with Specht and Burnside-Type Problems
• Mathematics
• 2014
We explore an approach to the celebrated Jacobian Conjecture by means of identities of algebras, initiated by the brilliant deceased mathematician, Alexander Vladimirovich Yagzhev (1951–2001), whoseExpand
Polynomial automorphisms, quantization and Jacobian conjecture related problems
• Mathematics
• 2019
The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as certain related topics.