Factorization semigroups and irreducible components of Hurwitz space

Details Factorization semigroups and irreducible components of Hurwitz space Factorization semigroups and irreducible components of Hurwitz space

2010-03-15

arxiv.org/abs/1003.2953v1

Mathematics

Algebraic Geometry

38 pages

Scientific paper

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 $d$ coverings of $\mathbb P^1$ 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.

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