Search results for " Weyl groups"

showing 2 items of 2 documents

On Hurwitz spaces of coverings with one special fiber

2009

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 s…

AlgebraCombinatoricsWeyl groupsymbols.namesakeMonodromyGeneral MathematicssymbolsPartition (number theory)Settore MAT/03 - GeometriaCentralizer and normalizerMathematicsHurwitz spaces connected components special fiber Weyl groups of type B_d
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On the irreducibility of Hurwitz spaces of coverings with an arbitrary number of special points

2013

In this paper we study Hurwitz spaces of coverings of Y with an arbitrary number of special points and with monodromy group a Weyl group of type D_d, where Y is a smooth, complex projective curve. We give conditions for which these spaces are irreducible.

Hurwitz spaces Weyl groups special points monodromy braid movesProjective curvePure mathematicsWeyl groupHurwitz quaternionGeneral MathematicsType (model theory)Algebrasymbols.namesakeMonodromyHurwitz's automorphisms theoremsymbolsIrreducibilitySettore MAT/03 - GeometriaMathematics::Representation TheoryMathematicsFilomat
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