6533b82ffe1ef96bd1295071
RESEARCH PRODUCT
On Hurwitz spaces of coverings with one special fiber
Francesca Vetrosubject
AlgebraCombinatoricsWeyl groupsymbols.namesakeMonodromyGeneral MathematicssymbolsPartition (number theory)Settore MAT/03 - GeometriaCentralizer and normalizerMathematicsHurwitz spaces connected components special fiber Weyl groups of type B_ddescription
Let X X' Y be a covering of smooth, projective complex curves such that p is a degree 2 etale covering and f is a degree d covering, with monodromy group Sd, branched in n + 1 points one of which is a special point whose local monodromy has cycle type given by the partition e = (e1,...,er) of d. We study such coverings whose monodromy group is either W(Bd) or wN(W(Bd))(G1)w-1 for some w in W(Bd), where W(Bd) is the Weyl group of type Bd, G1 is the subgroup of W(Bd) generated by reflections with respect to the long roots ei - ej and N(W(Bd))(G1) is the normalizer of G1. We prove that in both cases the corresponding Hurwitz spaces are not connected and hence are not irreducible. In fact, we show that if n + |e|= 2d, where |e| = ? i=1r(ei - 1), they have 22g - 1 connected components.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-03-04 |