Fixed points of polynomial automorphisms of $\mathrm{C}^n$

Abstract

We study the fixed point indices of some polynomial automorphisms of $\mathbf{C}^n$. In particular, it is shown that, for a composition of generalized Hénon maps, the sum of the fixed point indices vanishes. A consequence is that a generic polynomial automorphism of $\mathbf{C}^2$ has a saddle fixed point.