Search results for "32S22"

showing 2 items of 2 documents

Logarithmic bundles of deformed Weyl arrangements of type $A_2$

2016

We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given.

Pure mathematicsLogarithmic sheavesLogarithmMSC: 52C35 14F05 32S22General Mathematics010102 general mathematicsType (model theory)Weyl arrangements01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic GeometryComputer Science::GraphicsCorollary0103 physical sciencesFOS: Mathematics010307 mathematical physicsIsomorphism[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsRoot systemsLine arrangementsMSC 52C35 14F05 32S22Algebraic Geometry (math.AG)Mathematics
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A note on the Lawrence-Krammer-Bigelow representation

2002

A very popular problem on braid groups has recently been solved by Bigelow and Krammer, namely, they have found a faithful linear representation for the braid group B_n. In their papers, Bigelow and Krammer suggested that their representation is the monodromy representation of a certain fibration. Our goal in this paper is to understand this monodromy representation using standard tools from the theory of hyperplane arrangements. In particular, we prove that the representation of Bigelow and Krammer is a sub-representation of the monodromy representation which we consider, but that it cannot be the whole representation.

[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Pure mathematicsLinear representation[ MATH.MATH-GR ] Mathematics [math]/Group Theory [math.GR]Braid group20F36Group Theory (math.GR)52C3001 natural sciences[MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR]52C35Mathematics - Geometric TopologyMathematics::Group TheoryMathematics::Algebraic Geometry[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesFOS: Mathematics20F36 52C35 52C30 32S22braid groups0101 mathematicsMathematics::Representation TheoryComputingMilieux_MISCELLANEOUSMathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT][MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR]linear representations010102 general mathematicsRepresentation (systemics)FibrationSalvetti complexesGeometric Topology (math.GT)Mathematics::Geometric TopologyHyperplaneMonodromy010307 mathematical physicsGeometry and TopologyMathematics - Group Theory32S22
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