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Factorization semigroups and irreducible components of Hurwitz space
We introduce a natural structure of a semigroup (isomorphic to a
factorization semigroup of the unity in the symmetric group) on the set of
irreducible components of Hurwitz space of marked degree coverings of
of fixed ramification types. It is proved that this semigroup is
finitely presented. The problem when collections of ramification types define
uniquely the corresponding irreducible components of the Hurwitz space is
investigated. In particular, the set of irreducible components of the Hurwitz
space of three-sheeted coverings of the projective line is completely
described.Comment: 38 page
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