Search results for "Automorphisms"

showing 10 items of 24 documents

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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Hurwitz spaces of Galois coverings of P1, whose Galois groups are Weyl groups

2006

Abstract We prove the irreducibility of the Hurwitz spaces which parametrize equivalence classes of Galois coverings of P 1 , whose Galois group is an arbitrary Weyl group, and the local monodromies are reflections. This generalizes a classical theorem due to Luroth, Clebsch and Hurwitz.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryGalois cohomologyMathematics::Number TheoryFundamental theorem of Galois theoryGalois groupGalois moduleDifferential Galois theoryEmbedding problemsymbols.namesakeMathematics::Algebraic GeometryHurwitz's automorphisms theoremsymbolsGalois extensionMathematicsJournal of Algebra
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Symplectic automorphisms of prime order on K3 surfaces

2006

The aim of this paper is to study algebraic K3 surfaces (defined over the complex number field) with a symplectic automorphism of prime order. In particular we consider the action of the automorphism on the second cohomology with integer coefficients. We determine the invariant sublattice and its perpendicular complement, and show that the latter coincides with the Coxeter-Todd lattice in the case of automorphism of order three. We also compute many explicit examples, with particular attention to elliptic fibrations.

Discrete mathematicsPure mathematicsAutomorphismsAlgebra and Number TheoryOuter automorphism groupK3 surfacesAutomorphismCohomologyMathematics - Algebraic GeometryMathematics::Group TheoryInner automorphism14J28 14J10FOS: MathematicsInvariant (mathematics)Algebraic numberComplex numberAlgebraic Geometry (math.AG)ModuliSymplectic geometryMathematics
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A note on endomorphisms of hypercentral groups

2002

Abstract Let H be a subnormal subgroup of a hypercentral group G. We prove that endomorphisms of G are uniquely determined by their restrictions to H if and only if Hom(G/HG,G)=0, and draw some consequences from this fact.

Discrete mathematicsSubnormal subgroupAutomorphisms and endomorphisms of groupsPure mathematicsAlgebra and Number TheoryEndomorphismIf and only ifGroup (mathematics)Nilpotent and hypercentral groupsMathematicsJournal of Algebra
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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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Affine Surfaces With a Huge Group of Automorphisms

2013

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.

Normal subgrouprational fibrationsautomorphismsGroup (mathematics)General Mathematics010102 general mathematicsAutomorphism01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsMathematics::LogicMathematics - Algebraic GeometryMathematics::Group Theory0103 physical sciencesFree groupCountable setUncountable set[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics0101 mathematicsAlgebraic number14R25 14R20 14R05 14E05affine surfacesQuotientMathematicsInternational Mathematics Research Notices
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Locally tame plane polynomial automorphisms

2010

Abstract For automorphisms of a polynomial ring in two variables over a domain R , we show that local tameness implies global tameness provided that every 2-generated locally free R -module of rank 1 is free. We give examples illustrating this property.

PolynomialRank (linear algebra)Polynomial ringPolynomial automorphismsCommutative Algebra (math.AC)01 natural sciencesCombinatoricsMathematics - Algebraic GeometryFOS: MathematicsAlgebra en Topologie0101 mathematicsAlgebraic Geometry (math.AG)MathematicsAlgebra and TopologyAlgebra and Number TheoryPlane (geometry)local tameness010102 general mathematicsA domainMathematics - Commutative AlgebraAutomorphism[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]010101 applied mathematicsComputingMethodologies_DOCUMENTANDTEXTPROCESSING[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]14R10Journal of Pure and Applied Algebra
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Unbounded derivations and *-automorphisms groups of Banach quasi *-algebras

2018

This paper is devoted to the study of unbounded derivations on Banach quasi *-algebras with a particular emphasis to the case when they are infinitesimal generators of one parameter automorphisms groups. Both of them, derivations and automorphisms are considered in a weak sense; i.e., with the use of a certain families of bounded sesquilinear forms. Conditions for a weak *-derivation to be the generator of a *-automorphisms group are given.

Unbounded derivationPure mathematicsAutomorphisms groups and their infinitesimal generatorsInfinitesimalBanach quasi *-algebra01 natural sciencesMathematics::Group Theory*-Automorphisms groups and their infinitesimal generatorSettore MAT/05 - Analisi Matematica0103 physical sciencesFOS: MathematicsAutomorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivations; Automorphisms groups and their infinitesimal generators; Banach quasi; Integrability of derivation; Unbounded derivationsBanach quasi0101 mathematicsOperator Algebras (math.OA)MathematicsGroup (mathematics)Applied Mathematics010102 general mathematicsIntegrability of derivationMathematics - Operator AlgebrasAutomorphismUnbounded derivationsFunctional Analysis (math.FA)Mathematics - Functional AnalysisBounded function010307 mathematical physicsGenerator (mathematics)
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Automorphisms and abstract commensurators of 2-dimensional Artin groups

2004

In this paper we consider the class of 2-dimensional Artin groups with connected, large type, triangle-free defining graphs (type CLTTF). We classify these groups up to isomorphism, and describe a generating set for the automorphism group of each such Artin group. In the case where the defining graph has no separating edge or vertex we show that the Artin group is not abstractly commensurable to any other CLTTF Artin group. If, moreover, the defining graph satisfies a further `vertex rigidity' condition, then the abstract commensurator group of the Artin group is isomorphic to its automorphism group and generated by inner automorphisms, graph automorphisms (induced from automorphisms of the…

Vertex (graph theory)20F67CommensuratorCoxeter groupCoxeter group20F36InverseGroup Theory (math.GR)Automorphism2–dimensional Artin group20F36 20F55 20F65 20F67CombinatoricsMathematics::Group Theorytriangle freeGenerating set of a groupFOS: Mathematicscommensurator groupArtin groupGeometry and TopologyIsomorphism20F5520F65graph automorphismsMathematics - Group TheoryMathematics
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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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