Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Totally free arrangements of hyperplanes

Author(s): Takuro Abe; Hiroaki Terao; Masahiko Yoshinaga
Journal: Proc. Amer. Math. Soc. 137 (2009), 1405-1410.
MSC (2000): Primary 32S22
Posted: November 5, 2008
MathSciNet review: 2465666
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Abstract: A central arrangement $\mathcal{A}$ of hyperplanes in an $\ell$ -dimensional vector space is said to be totally free if a multiarrangement $(\mathcal{A}, m)$ is free for any multiplicity $m : \mathcal{A}\rightarrow \Z_{> 0}$ . It has been known that $\mathcal{A}$ is totally free whenever $\ell \le 2$ . In this article, we will prove that there does not exist any totally free arrangement other than the obvious ones, that is, a product of one-dimensional arrangements and two-dimensional ones.

References:

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