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Bulletin of the London Mathematical Society 2005 37(1):126-134; doi:10.1112/S0024609304003704
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© London Mathematical Society

On the Freeness of 3-Arrangements

Masahiko Yoshinaga

Research Institute for Mathematical Sciences, Kyoto University Kyoto 606-8502, Japan; yosinaga{at}kurims.kyoto-u.ac.jp

Received 24 June 2003. Revision received 2 December 2003.

Hyperplane arrangements in a three-dimensional vector space are considered in this paper. A characterization of the freeness of such an arrangement is given in terms of the characteristic polynomial and a restricted multiarrangement. As an application, the freeness of cones over certain two-dimensional affine arrangements is proved. 2000 Mathematics Subject Classification 52C35 (primary), 32S22 (secondary).


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