### Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type ${B}_{d}$

Let $X$, ${X}^{\prime}$, $Y$ be smooth projective complex curves with $Y$ curve of genus $\ge 1$. Let $d$ be an integer $\ge 3$, let $\underset{\xaf}{e}=({e}_{1},\mathrm{\dots},{e}_{r})$ be a partition of $d$ and let $|e|={\sum}_{i=1}^{r}({e}_{i}-1)$. Let $X\stackrel{\mathit{\pi}}{\to}{X}^{\prime}\stackrel{\mathit{f}}{\to}Y$ be a sequence of coverings where $\pi $ is a degree 2 branched covering and $f$ is a degree $d$ covering, with monodromy group ${S}_{d}$, branched in ${n}_{2}+1$ points, one of which is special point $c$ whose local monodromy has cycle type given by $\underset{\xaf}{e}$. Moreover the branch locus of the covering $\pi $ is contained in ${f}^{-1}(c)$. In this paper we prove the irreducibility of the Hurwitz...