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

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

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All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Cite this

Abe, T., & Kühne, L. (2018). Heavy hyperplanes in multiarrangements and their freeness. Journal of Algebraic Combinatorics, 48(4), 581-606. https://doi.org/10.1007/s10801-017-0806-y

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Access to Document

10.1007/s10801-017-0806-y