Geodesic
Factorization semigroups and irreducible components of the Hurwitz space
Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 711-748

Voir la notice de l'article provenant de la source Math-Net.Ru

We introduce a natural structure of a semigroup (isomorphic to the factorization semigroup of the identity in the symmetric group) on the set of irreducible components of the Hurwitz space of coverings of marked degree $d$ of $\mathbb P^1$ of fixed ramification types. We shall prove that this semigroup is finitely presented. We study the problem of when collections of ramification types uniquely determine the corresponding irreducible components of the Hurwitz space. In particular, we give a complete description of the set of irreducible components of the Hurwitz space of three-sheeted coverings of the projective line.
Keywords: semigroup, factorization of an element of a group, irreducible components of the Hurwitz space. 
@article{IM2_2011_75_4_a3,
     author = {Vik. S. Kulikov},
     title = {Factorization semigroups and irreducible components of the {Hurwitz} space},
     journal = {Izvestiya. Mathematics },
     pages = {711--748},
     publisher = {mathdoc},
     volume = {75},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a3/}
}
TY  - JOUR
AU  - Vik. S. Kulikov
TI  - Factorization semigroups and irreducible components of the Hurwitz space
JO  - Izvestiya. Mathematics 
PY  - 2011
SP  - 711
EP  - 748
VL  - 75
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a3/
LA  - en
ID  - IM2_2011_75_4_a3
ER  - 
%0 Journal Article
%A Vik. S. Kulikov
%T Factorization semigroups and irreducible components of the Hurwitz space
%J Izvestiya. Mathematics 
%D 2011
%P 711-748
%V 75
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a3/
%G en
%F IM2_2011_75_4_a3
Vik. S. Kulikov. Factorization semigroups and irreducible components of the Hurwitz space. Izvestiya. Mathematics , Tome 75 (2011) no. 4, pp. 711-748. http://geodesic.mathdoc.fr/item/IM2_2011_75_4_a3/