Free arrangements and coefficients of characteristic polynomials

Takuro Abe, Masahiko Yoshinaga

Research output: Contribution to journalArticle

13 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 languageEnglish
Pages (from-to)911-919
Number of pages9
JournalMathematische Zeitschrift
Volume275
Issue number3-4
DOIs
Publication statusPublished - Dec 1 2013
Externally publishedYes

Fingerprint

Characteristic polynomial
Arrangement
Coefficient
Betti numbers
Reverse

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Free arrangements and coefficients of characteristic polynomials. / Abe, Takuro; Yoshinaga, Masahiko.

In: Mathematische Zeitschrift, Vol. 275, No. 3-4, 01.12.2013, p. 911-919.

Research output: Contribution to journalArticle

Abe, Takuro ; Yoshinaga, Masahiko. / Free arrangements and coefficients of characteristic polynomials. In: Mathematische Zeitschrift. 2013 ; Vol. 275, No. 3-4. pp. 911-919.
@article{b56ea3df535b4a5cadc9c1b0866d4983,
title = "Free arrangements and coefficients of characteristic polynomials",
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.",
author = "Takuro Abe and Masahiko Yoshinaga",
year = "2013",
month = "12",
day = "1",
doi = "10.1007/s00209-013-1165-6",
language = "English",
volume = "275",
pages = "911--919",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer New York",
number = "3-4",

}

TY - JOUR

T1 - Free arrangements and coefficients of characteristic polynomials

AU - Abe, Takuro

AU - Yoshinaga, Masahiko

PY - 2013/12/1

Y1 - 2013/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84888132987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888132987&partnerID=8YFLogxK

U2 - 10.1007/s00209-013-1165-6

DO - 10.1007/s00209-013-1165-6

M3 - Article

AN - SCOPUS:84888132987

VL - 275

SP - 911

EP - 919

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3-4

ER -