Search results for "local monodromies"
showing 2 items of 2 documents
Irreducibility of Hurwitz spaces of coverings with one special fiber
2006
Abstract Let Y be a smooth, projective complex curve of genus g ⩾ 1. Let d be an integer ⩾ 3, let e = {e1, e2,..., er} be a partition of d and let | e | = Σi=1r(ei − 1). In this paper we study the Hurwitz spaces which parametrize coverings of degree d of Y branched in n points of which n − 1 are points of simple ramification and one is a special point whose local monodromy has cyclic type e and furthermore the coverings have full monodromy group Sd. We prove the irreducibility of these Hurwitz spaces when n − 1 + | e | ⩾ 2d, thus generalizing a result of Graber, Harris and Starr [A note on Hurwitz schemes of covers of a positive genus curve, Preprint, math. AG/0205056].
Irreducibility of Hurwitz spaces of coverings with monodromy groups Weyl groups of type W(B_d)
2007
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 ).