Logarithmic bundles of deformed Weyl arrangements of type $A_2$

Takuro Abe (1) , Daniele Faenzi (2) , Jean Vallès (3)

1 Department of Mechanical Engineering and Science, Kyoto University
2 Algèbre et géométrie
3 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We consider generalized deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements, well-known to be free. We study all the 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.

Mots clés: Line arrangements; Logarithmic sheaves; Weyl arrangements; Root systems

Domaines: Géométrie algébrique [math.AG]

Takuro Abe, Daniele Faenzi, Jean Vallès. Logarithmic bundles of deformed Weyl arrangements of type $A_2$. 2014. ⟨hal-00987021v2⟩