# Some families of polynomial automorphisms III

Published in *Journal of Pure and Applied Algebra*, 2015

Recommended citation:

E. Edo & **D. Lewis**, Some families of polynomial automorphisms III, *Journal of Pure and Applied Algebra*, 219, no. 4 (2015), 864-874.

### Abstract

We prove that the closure (for the Zariski topology) of the set of polynomial automorphisms of the complex affine plane whose polydegree is $(cd-1,b,a)$ contains all automorphisms of polydegree $(cd+a)$ where $a,b \geq 2$ and $c\geq 1$ are integers and $d=ab-1$. When $b=2$, this result gives a family of counterexamples to a conjecture of Furter.