The Stability of the Family of B 2-Type Arrangements |
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| Authors: | Takuro Abe |
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| Affiliation: | 1. Department of Mathematics , Kyoto University , Kyoto , Japan abetaku@math.kyoto-u.ac.jp |
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| Abstract: | We introduce the family of B 2-type arrangements as a generalization of the classical Coxeter arrangement of type B 2 and consider the stability and the freeness of it. We show the freeness and (semi)stability are determined by the combinatorics. Moreover, we give a partial answer to the 4-shift problem, which is a conjecture on the combinatorics and geometry induced from the B 2-type arrangements. |
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| Keywords: | Coxeter arrangement Hyperplane arrangements Logarithmic vector fields |
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