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.
"Weighted multidegrees of polynomial automorphisms over a domain." J. Math. Soc. Japan 68 (1) 119 - 149, January, 2016. https://doi.org/10.2969/jmsj/06810119