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# Totally free arrangements of hyperplanes

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 Title: Totally free arrangements of hyperplanes Authors: Abe, Takuro Browse this author Terao, Hiroaki Browse this author Yoshinaga, Masahiko Browse this author Issue Date: 22-May-2008 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 915 Start Page: 1 End Page: 7 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69722 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics