Free arrangements and coefficients of characteristic polynomials

Takuro Abe; Masahiko Yoshinaga

doi:10.1007/s00209-013-1165-6

Free arrangements and coefficients of characteristic polynomials

Takuro Abe, Masahiko Yoshinaga

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

14 Citations (Scopus)

Abstract

Ziegler showed that the multirestriction of a free arrangement is also free. After Ziegler's work, several results concerning the "reverse direction", i.e., characterizing freeness of an arrangement via that of its multirestriction, have appeared. In this paper, we prove a new characterization of freeness in which the second Betti number of the arrangement plays a crucial role.

Original language	English
Pages (from-to)	911-919
Number of pages	9
Journal	Mathematische Zeitschrift
Volume	275
Issue number	3-4
DOIs	https://doi.org/10.1007/s00209-013-1165-6
Publication status	Published - Dec 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/s00209-013-1165-6

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AU - Yoshinaga, Masahiko

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AB - Ziegler showed that the multirestriction of a free arrangement is also free. After Ziegler's work, several results concerning the "reverse direction", i.e., characterizing freeness of an arrangement via that of its multirestriction, have appeared. In this paper, we prove a new characterization of freeness in which the second Betti number of the arrangement plays a crucial role.

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DO - 10.1007/s00209-013-1165-6

M3 - Article

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JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3-4

ER -

Free arrangements and coefficients of characteristic polynomials

Abstract

All Science Journal Classification (ASJC) codes

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