Weighted multidegrees of polynomial automorphisms over a domain
Shigeru Kuroda

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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons
