Factorization semigroups and irreducible components of the Hurwitz space. II
Izvestiya. Mathematics, Tome 76 (2012) no. 2, pp. 356-364
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We continue the investigation started in [1]. Let $\mathrm{HUR}_{d,t}^{\mathcal S_d}(\mathbb P^1)$ be the Hurwitz space of coverings of degree $d$ of the projective line $\mathbb P^1$ with Galois group $\mathcal S_d$ and monodromy type $t$. The monodromy type is a set of local monodromy types, which are defined as conjugacy classes of permutations $\sigma$ in the symmetric group $\mathcal S_d$ acting on the set $I_d=\{1,\dots,d\}$. We prove that if the type $t$ contains sufficiently many local monodromies belonging to the conjugacy class $C$ of an odd permutation $\sigma$ which leaves $f_C\geqslant 2$ elements of $I_d$ fixed, then the Hurwitz space $\mathrm{HUR}_{d,t}^{\mathcal S_d}(\mathbb P^1)$ is irreducible.
Keywords:
semigroup, factorizations of an element of a group, irreducible components of the Hurwitz space.
@article{IM2_2012_76_2_a5,
author = {Vik. S. Kulikov},
title = {Factorization semigroups and irreducible components of the {Hurwitz} {space.~II}},
journal = {Izvestiya. Mathematics},
pages = {356--364},
year = {2012},
volume = {76},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a5/}
}
Vik. S. Kulikov. Factorization semigroups and irreducible components of the Hurwitz space. II. Izvestiya. Mathematics, Tome 76 (2012) no. 2, pp. 356-364. http://geodesic.mathdoc.fr/item/IM2_2012_76_2_a5/