Totally free arrangements of hyperplanes

Takuro Abe; Hiroaki Terao; Masahiko Yoshinaga

doi:10.1090/S0002-9939-08-09755-4

Totally free arrangements of hyperplanes

Takuro Abe, Hiroaki Terao, Masahiko Yoshinaga

Research output: Contribution to journal › Article › peer-review

8 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 language	English
Pages (from-to)	1405-1410
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-08-09755-4
Publication status	Published - Apr 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-08-09755-4

Cite this

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AB - 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.

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Totally free arrangements of hyperplanes

Abstract

All Science Journal Classification (ASJC) codes

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