# Totally free arrangements of hyperplanes

Preprint Series # 915
Abe, Takuro and Terao, Hiroaki and Yoshinaga, Masahiko Totally free arrangements of hyperplanes. (2008);

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## Abstract

A 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 one-dimensional arrangements and two-dimensional ones.

Item Type: Preprint 30 totally free arrangements, multiarrangements, arrangements of hyperplanes 32-xx SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES 1863