Totally free arrangements of hyperplanes

Details Totally free arrangements of hyperplanes Totally free arrangements of hyperplanes

2008-05-15

arxiv.org/abs/0805.2243v3

Proc. AMS 137 (2009), 1405-1410

Mathematics

Commutative Algebra

7 pages

Scientific paper

A central arrangement $\A$ of hyperplanes in an $\ell$-dimensional vector space $V$ is said to be {\it totally free} if a multiarrangement $(\A, m)$ is free for any multiplicity $ m : \A\to \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.

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