The genus of the configuration spaces for Artin groups of affne type

Let $(\mathbf W,S)$ be a Coxeter system, $S$ finite, and let $\mathbf G_{\mathbf W}$ be the associated Artin group. One has {\it configuration spaces} $\mathbf Y,\ \mathbf Y_{\mathbf W},$ where $\mathbf G_{\mathbf W}=\pi_1(\mathbf Y_{\mathbf W}),$ and a natural $\mathbf W$-covering $f_{\mathbf W}:\ \mathbf Y\to\mathbf Y_{\mathbf W}.$ The {\it Schwarz genus} $g(f_{\mathbf W})$ is a natural topological invariant to consider. In \cite{salvdec2} it was computed for all finite-type Artin groups, with the exception of case $A_n$ (for which see \cite{vassiliev},\cite{salvdecproc3}).