2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164216Let $K[x,y]$ be the polynomial algebra in two variables over an algebraically closed field $K$. We generalize to the case of any characteristic the result of Furter that over a field of characteristic zero the set of automorphisms $(f,g)$ of $K[x,y]$ such that $\max\{\text{deg}(f),\text{deg}(g)\}=n\geq 2$ is constructible with dimension $n+6$. The same result holds for the automorphisms of the free associative algebra $K< x,y>$. We have also obtained analogues for free algebras with two generators in Nielsen -- Schreier varieties of algebras.10 pagesAlgebraic GeometryCommutative Algebra13B25; 16S10; 17A50text