Tame automorphisms of C^3 with multidegree of the form (3,d_2,d_3)
Marek Karas
TL;DR
This paper characterizes when a multidegree sequence of the form (3,d_2,d_3) corresponds to a tame automorphism of C^3, based on divisibility and linear combination conditions.
Contribution
It provides a complete characterization of multidegree sequences (3,d_2,d_3) for tame automorphisms of C^3, linking algebraic conditions to automorphism properties.
Findings
Multidegree sequence (3,d_2,d_3) corresponds to a tame automorphism if 3 divides d_2 or d_3 is a linear combination of 3 and d_2.
The characterization is both necessary and sufficient.
The result clarifies the structure of tame automorphisms with specific multidegree patterns.
Abstract
In this note we prove that the sequence (3,d_2,d_3), where d_3>= d_2>= 3, is the multidegee of some tame automorphism of C^3, if and only if 3|d_2 or d_3 is a linaer combination of 3 and d_2 with coefficients in N.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Coding theory and cryptography · Mathematical Dynamics and Fractals