Totally free arrangements of hyperplanes
Preprint Series # 915 Abe, Takuro and Terao, Hiroaki and Yoshinaga, Masahiko Totally free arrangements of hyperplanes. (2008); AbstractA central arrangement $\A$ of hyperplanes in an $\ell$dimensional
vector space $V$ is said to be totally free}if a multiarrangement if
$(\A, m)$ is free for any multiplicity $ m : \A\rightarrow \Z_{> 0}$.
It has been known that $\A$ 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
onedimensional arrangements and twodimensional ones.
