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This article is cited in 5 scientific papers (total in 5 papers)
Factorization semigroups and irreducible components of the Hurwitz space. II
Vik. S. Kulikov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
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.
Received: 16.11.2010 Revised: 23.08.2011
Citation:
Vik. S. Kulikov, “Factorization semigroups and irreducible components of the Hurwitz space. II”, Izv. Math., 76:2 (2012), 356–364
Linking options:
https://www.mathnet.ru/eng/im5886https://doi.org/10.1070/IM2012v076n02ABEH002586 https://www.mathnet.ru/eng/im/v76/i2/p151
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Abstract page: | 534 | Russian version PDF: | 172 | English version PDF: | 12 | References: | 51 | First page: | 16 |
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