Proper holomorphic mappings between rigid polynomial domains in $\mathbb{C}^{n+1}$
Proper holomorphic mappings between rigid polynomial domains in $\mathbb{C}^{n+1}$
We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in C n+1 .It appears, in particular, that it is controlled only by the first domain.As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.