Heavy hyperplanes in multiarrangements and their freeness

Takuro Abe; Lukas Kühne

doi:10.1007/s10801-017-0806-y

Heavy hyperplanes in multiarrangements and their freeness

Takuro Abe, Lukas Kühne

Division of Fundamental mathematics

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

1 Citation (Scopus)

Abstract

Only few categories of free arrangements are known in which Terao’s conjecture holds. One such category consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga’s freeness criterion, to unbalanced multiarrangements.

Original language	English
Pages (from-to)	581-606
Number of pages	26
Journal	Journal of Algebraic Combinatorics
Volume	48
Issue number	4
DOIs	https://doi.org/10.1007/s10801-017-0806-y
Publication status	Published - Dec 1 2018

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-017-0806-y

Fingerprint Dive into the research topics of 'Heavy hyperplanes in multiarrangements and their freeness'. Together they form a unique fingerprint.

Cite this

@article{ac1c5dfe2edd4cc4a61684d040ee7a63,

title = "Heavy hyperplanes in multiarrangements and their freeness",

abstract = "Only few categories of free arrangements are known in which Terao{\textquoteright}s conjecture holds. One such category consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga{\textquoteright}s freeness criterion, to unbalanced multiarrangements.",

author = "Takuro Abe and Lukas K{\"u}hne",

year = "2018",

month = dec,

day = "1",

doi = "10.1007/s10801-017-0806-y",

language = "English",

volume = "48",

pages = "581--606",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - Heavy hyperplanes in multiarrangements and their freeness

AU - Abe, Takuro

AU - Kühne, Lukas

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Only few categories of free arrangements are known in which Terao’s conjecture holds. One such category consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga’s freeness criterion, to unbalanced multiarrangements.

AB - Only few categories of free arrangements are known in which Terao’s conjecture holds. One such category consists of 3-arrangements with unbalanced Ziegler restrictions. In this paper, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criterions for simple arrangements, including Yoshinaga’s freeness criterion, to unbalanced multiarrangements.

UR - http://www.scopus.com/inward/record.url?scp=85037333866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85037333866&partnerID=8YFLogxK

U2 - 10.1007/s10801-017-0806-y

DO - 10.1007/s10801-017-0806-y

M3 - Article

AN - SCOPUS:85037333866

VL - 48

SP - 581

EP - 606

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

SN - 0925-9899

IS - 4

ER -