Hurwitz spaces of coverings with two special fibers and monodromy group a Weyl group of type B_d

Francesca Vetro

Vol. 255 (2012), No. 1, 241–255

DOI: 10.2140/pjm.2012.255.241

Abstract

Let d ≥ 3, n₁ > 0 and n₂ > 0 be integers. Let e = (e₁,…,e_r) and q = (q₁,…,q_s) be two partitions of d. Let X,X′ and Y be smooth, connected, projective complex curves. In this paper we study coverings that decompose into a sequence

where π is a degree-two coverings with n₁ branch points and branch locus D_π and f is a degree-d coverings with n₂ points of simple branching and two special points whose local monodromy is given by e and q , respectively. Furthermore the covering f has monodromy group S_d and f(D_π) ∩D_f = ∅ where D_f denotes the branch locus of f. We prove that the corresponding Hurwitz spaces are irreducible under the hypothesis n₂ − s − r ≥ d + 1.

Keywords

Hurwitz spaces, special fibers, branched coverings, Weyl group of type B_d, monodromy, braid moves

Mathematical Subject Classification 2010

Primary: 14H30

Secondary: 14H10

Milestones

Received: 1 February 2011

Accepted: 31 October 2011

Published: 14 March 2012