Totally free arrangements of hyperplanes

Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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
Volume137
Issue number4
DOIs
Publication statusPublished - Apr 1 2009
Externally publishedYes

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Arrangement of Hyperplanes
Vector spaces
Arrangement
Hyperplane
Vector space
Multiplicity

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

Totally free arrangements of hyperplanes. / Abe, Takuro; Terao, Hiroaki; Yoshinaga, Masahiko.

In: Proceedings of the American Mathematical Society, Vol. 137, No. 4, 01.04.2009, p. 1405-1410.

Research output: Contribution to journalArticle

Abe, Takuro ; Terao, Hiroaki ; Yoshinaga, Masahiko. / Totally free arrangements of hyperplanes. In: Proceedings of the American Mathematical Society. 2009 ; Vol. 137, No. 4. pp. 1405-1410.
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