Weighted multidegrees of polynomial automorphisms over a domain

TL;DR

This paper explores the properties of weighted multidegrees of polynomial automorphisms using a new approach centered on stable coordinates, with applications to the generalized Shestakov-Umirbaev theory.

Contribution

It introduces a novel method for analyzing weighted multidegrees of polynomial automorphisms via stable coordinates, expanding the theoretical framework.

Findings

New insights into weighted multidegrees

Applications to generalized Shestakov-Umirbaev theory

Enhanced understanding of polynomial automorphisms

Abstract

The notion of the weighted degree of a polynomial is a basic tool in Affine Algebraic Geometry. In this paper, we study the properties of the weighted multidegrees of polynomial automorphisms by a new approach which focuses on stable coordinates. We also present some applications of the generalized Shestakov-Umirbaev theory.