### 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 | |

Publication status | Published - Apr 1 2009 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(4), 1405-1410. https://doi.org/10.1090/S0002-9939-08-09755-4

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 4, pp. 1405-1410. https://doi.org/10.1090/S0002-9939-08-09755-4

}

TY - JOUR

T1 - Totally free arrangements of hyperplanes

AU - Abe, Takuro

AU - Terao, Hiroaki

AU - Yoshinaga, Masahiko

PY - 2009/4/1

Y1 - 2009/4/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=77950542187&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950542187&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09755-4

DO - 10.1090/S0002-9939-08-09755-4

M3 - Article

AN - SCOPUS:77950542187

VL - 137

SP - 1405

EP - 1410

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -