Totally free arrangements of hyperplanes-Reference-Cited by-同舟云学术

Totally free arrangements of hyperplanes

Published:2008-11-05 Issue:4 Volume:137 Page:1405-1410
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Abe Takuro,Terao Hiroaki,Yoshinaga Masahiko

Abstract

A central arrangement A \mathcal {A} of hyperplanes in an ℓ \ell -dimensional vector space V V is said to be totally free if a multiarrangement ( A , m ) (\mathcal {A}, m) is free for any multiplicity m : A → Z > 0 m : \mathcal {A}\rightarrow \mathbb {Z} _{> 0} . It has been known that A \mathcal {A} is totally free whenever ℓ ≤ 2 \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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2009-137-04/S0002-9939-08-09755-4/S0002-9939-08-09755-4.pdf

Reference12 articles.

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3. The characteristic polynomial of a multiarrangement;Abe, Takuro;Adv. Math.,2007

4. The Euler multiplicity and addition-deletion theorems for multiarrangements;Abe, Takuro;J. Lond. Math. Soc. (2),2008

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