0000000000298082

AUTHOR

Takuro Abe

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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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