Automorphisms of $\mathbb{C}[x_1, \dots, x_n]$

Question

Are the linear transformations, and the automorphisms of the form $\sigma(x_1, \dots, x_n) = (x_1 -f(x_2, \dots, x_n), x_2, \dots, x_n)$, where $f$ is a polynomial, generators of the group of automorphisms of $\mathbb{C}[x_1, \dots, x_n]$?

If this is true, where can I find a good reference?

Thanks in advance.

Answer 1

The answer is apparently yes for $n = 2$ but no for $n = 3$. See this paper.