Irreducibility of Hurwitz spaces of coverings with monodromy groups Weyl groups of type W(B_d)

Let Y be a smooth, connected, projective complex curve of genus ≥0. R. Biggers and M. Fried [J. Reine Angew. Math. 335, 87–121 (1982; Zbl 0484.14002), Trans. Am. Math. Soc. 295, No. 1, 59–70 (1986; Zbl 0601.14022)] proved the irreducibility of the Hurwitz spaces which parametrize coverings of ℙ 1 whose monodromy group is a Weyl of type W(D d ). Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type W(B d ).