Deletion theorem and combinatorics of hyperplane arrangements

研究成果: ジャーナルへの寄稿記事

抄録

We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give a sufficient and necessary condition for the deletion theorem in terms of characteristic polynomials. As a corollary, we prove that whether a free arrangement has a free filtration is also combinatorial. The proof is based on the result about a minimal set of generators of a logarithmic derivation module of a multiarrangement which satisfies the b 2 -equality.

元の言語英語
ページ(範囲)581-595
ページ数15
ジャーナルMathematische Annalen
373
発行部数1-2
DOI
出版物ステータス出版済み - 2 8 2019

Fingerprint

Arrangement of Hyperplanes
Combinatorics
Deletion
Arrangement
Theorem
Minimal Set
Characteristic polynomial
Hyperplane
Filtration
Corollary
Logarithmic
Equality
Intersection
Generator
Necessary Conditions
Module
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

Deletion theorem and combinatorics of hyperplane arrangements. / Abe, Takuro.

:: Mathematische Annalen, 巻 373, 番号 1-2, 08.02.2019, p. 581-595.

研究成果: ジャーナルへの寄稿記事

@article{77e5a05860694a7a8e78d5133a072fd7,
title = "Deletion theorem and combinatorics of hyperplane arrangements",
abstract = "We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give a sufficient and necessary condition for the deletion theorem in terms of characteristic polynomials. As a corollary, we prove that whether a free arrangement has a free filtration is also combinatorial. The proof is based on the result about a minimal set of generators of a logarithmic derivation module of a multiarrangement which satisfies the b 2 -equality.",
author = "Takuro Abe",
year = "2019",
month = "2",
day = "8",
doi = "10.1007/s00208-018-1713-9",
language = "English",
volume = "373",
pages = "581--595",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
number = "1-2",

}

TY - JOUR

T1 - Deletion theorem and combinatorics of hyperplane arrangements

AU - Abe, Takuro

PY - 2019/2/8

Y1 - 2019/2/8

N2 - We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give a sufficient and necessary condition for the deletion theorem in terms of characteristic polynomials. As a corollary, we prove that whether a free arrangement has a free filtration is also combinatorial. The proof is based on the result about a minimal set of generators of a logarithmic derivation module of a multiarrangement which satisfies the b 2 -equality.

AB - We show that the deletion theorem of a free arrangement is combinatorial, i.e., whether we can delete a hyperplane from a free arrangement keeping freeness depends only on the intersection lattice. In fact, we give a sufficient and necessary condition for the deletion theorem in terms of characteristic polynomials. As a corollary, we prove that whether a free arrangement has a free filtration is also combinatorial. The proof is based on the result about a minimal set of generators of a logarithmic derivation module of a multiarrangement which satisfies the b 2 -equality.

UR - http://www.scopus.com/inward/record.url?scp=85048668730&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048668730&partnerID=8YFLogxK

U2 - 10.1007/s00208-018-1713-9

DO - 10.1007/s00208-018-1713-9

M3 - Article

AN - SCOPUS:85048668730

VL - 373

SP - 581

EP - 595

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1-2

ER -