On multidegrees of polynomial automorphisms of C^3

TL;DR

This paper proves that for any pair of positive integers, there exists a threshold beyond which one can construct tame polynomial automorphisms of ^3 with prescribed multidegrees, demonstrating flexibility in their degree structures.

Contribution

It establishes the existence of tame polynomial automorphisms of ^3 with arbitrary large third degree component for any fixed pair of degrees, advancing understanding of multidegree configurations.

Findings

Existence of automorphisms with prescribed multidegrees beyond a certain threshold.

Demonstrates the construction of tame automorphisms with specific degree patterns.

Provides a foundation for further exploration of multidegree properties in polynomial automorphisms.

Abstract

We prove that for every pair of positive integers a, b there exists a number c_0 such that for every c>=c_0 one can find a tame polynomial automorphism of C^3 with multidegree equal to (a,b,c).