Free arrangements and coefficients of characteristic polynomials |
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| Authors: | Takuro Abe Masahiko Yoshinaga |
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| Institution: | 1. Department of Mechanical Engineering and Science, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto, 6068501, Japan
2. Department of Mathematics, Hokkaido University, Kita 10 Nishi 8, Kita-Ku, Sapporo, 0600810, Japan
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| Abstract: | Ziegler showed that the multirestriction of a free arrangement is also free. After Ziegler’s work, several results concerning the “reverse direction”, i.e., characterizing freeness of an arrangement via that of its multirestriction, have appeared. In this paper, we prove a new characterization of freeness in which the second Betti number of the arrangement plays a crucial role. |
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