Geodesic
A note on coverings with special fibres and monodromy group $S_{d}$
Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1110-1115

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We consider branched coverings of degree $d$ over $Y$ with monodromy group $S_{d}$, $k$ points of simple branching, $n-k$ special points and fixed branching data at the special points, where $Y$ is a smooth connected complex projective curve of genus $g\geqslant1$, and $n$, $k$ are integers with $n>k>0$. We prove that the corresponding Hurwitz spaces are irreducible if $k>3d-3$.
Keywords: Hurwitz spaces, special fibres, branched coverings, braid moves.
Mots-clés : monodromy 
@article{IM2_2012_76_6_a2,
     author = {F. Vetro},
     title = {A note on coverings with special fibres and monodromy group $S_{d}$},
     journal = {Izvestiya. Mathematics },
     pages = {1110--1115},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a2/}
}
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F. Vetro. A note on coverings with special fibres and monodromy group $S_{d}$. Izvestiya. Mathematics , Tome 76 (2012) no. 6, pp. 1110-1115. http://geodesic.mathdoc.fr/item/IM2_2012_76_6_a2/