Totally free arrangements of hyperplanes

Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A central arrangement A of hyperplanes in an ℓ-dimensional vector space V is said to be totally free if a multiarrangement (A, m) is free for any multiplicity m : A → ℤ>0. It has been known that A is totally free whenever ℓ ≤ 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.

Original languageEnglish
Pages (from-to)1405-1410
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number4
Publication statusPublished - Apr 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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