6533b7d7fe1ef96bd126842c

RESEARCH PRODUCT

Logarithmic bundles of deformed Weyl arrangements of type $A_2$

Takuro AbeDaniele FaenziJean Vallès

subject

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

description

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.

yearjournalcountryeditionlanguage
2016-01-01
https://hal.archives-ouvertes.fr/hal-01050441