On multidegrees of polynomial automorphisms of C^3
Jakub Zygad{\l}o

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).
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Meromorphic and Entire Functions · Algebraic Geometry and Number Theory
