Dept. Math, Hokkaido Univ. EPrints Server

The stability of the family of $B_2$-type arrangements

Preprint Series # 790
Abe, Takuro The stability of the family of $B_2$-type arrangements. (2006);

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We introduce a $B_2$-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 their (semi)stability is determined by the combinatorics. Moreover, we give a partial answer to the $4$-shift problem, which is the conjecture on the combinatorics and geometry induced from $B_2$-type arrangements.

Item Type:Preprint
Additional Information:40
Uncontrolled Keywords:hyperplane arrangement, Coxeter group, stable vector bundle, splitting of vector bundle
ID Code:1547