Search results for "Hurwitz quaternion"

showing 4 items of 4 documents

Irreducible components of Hurwitz spaces of coverings with two special fibers

2013

In this paper we prove new results of irreducibility for Hurwitz spaces of coverings whose monodromy group is a Weyl group of type B_d and whose local monodromies are all reflections except two.

Weyl groupPure mathematicsHurwitz quaternionGroup (mathematics)General MathematicsType (model theory)Hurwitz spaces special fibers branched coverings Weyl group of type B_d monodromy braid moves.symbols.namesakeMathematics::Algebraic GeometryMonodromyHurwitz's automorphisms theoremsymbolsIrreducibilitySettore MAT/03 - GeometriaMathematics::Representation TheoryMathematics
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Transitive factorizations in the hyperoctahedral group

2008

The classical Hurwitz enumeration problem has a presentation in terms of transitive factor- izationsin the symmetric group. This presentationsuggestsageneralizationfromtypeAto otherfinite reflection groups and, in particular, to type B.W e study this generalization both from ac ombinatorial and a geometric point of view, with the prospect of providing am eans of understanding more of the structure of the moduli spaces of maps with an S2-symmetry. The type A case has been well studied and connects Hurwitz numbers to the moduli space of curves. W ec onjecture an analogous setting for the type B case that is studied here. 1I ntroduction Transitive factorizations of permutations into transposit…

CombinatoricsAlgebraic combinatoricsHurwitz quaternionHurwitz problemSymmetric groupGeneral MathematicsHurwitz's automorphisms theoremHurwitz matrixHurwitz polynomialSettore MAT/03 - GeometriaHyperoctahedral groupMathematicssymmetric group covering space
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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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Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus

2014

Let Y be a smooth, projective, irreducible complex curve. A G-covering p : C → Y is a Galois covering, where C is a smooth, projective, irreducible curve and an isomorphism G ∼ −→ Aut(C/Y ) is fixed. Two G-coverings are equivalent if there is a G-equivariant isomorphism between them. We are concerned with the Hurwitz spaces H n (Y ) and H G n (Y, y0). The first one parameterizes Gequivalence classes of G-coverings of Y branched in n points. The second one, given a point y0 ∈ Y , parameterizes G-equivalence classes of pairs [p : C → Y, z0], where p : C → Y is a G-covering unramified at y0 and z0 ∈ p (y0). When G = Sd one can equivalently consider coverings f : X → Y of degree d with full mon…

Discrete mathematicsHurwitz quaternionHurwitz space Galois covering Braid groupGalois cohomologyInverse Galois problemGeneral MathematicsGalois groupSplitting of prime ideals in Galois extensionsEmbedding problemCombinatoricsHurwitz's automorphisms theoremGalois extensionSettore MAT/03 - GeometriaMathematics
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