Abstract
Let Y be a smooth, connected, projective complex curve. In this paper, we study the Hurwitz spaces which parameterize branched coverings of Y whose monodromy group is a Weyl group of type Dd and whose local monodromies are all reflections except one. We prove the irreducibility of these spaces when \(Y \simeq \mathbb {P}^{1}\) and successively we extend the result to curves of genus g ≥ 1.
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