TY - JOUR
T1 - Heavy hyperplanes in multiarrangements and their freeness
AU - Abe, Takuro
AU - Kühne, Lukas
N1 - Funding Information:
The first author is partially supported by JSPS Grant-in-Aid for Young Scientists (B) No. 24740012. The main part of this work was done during a research stay of the second author at Kyoto University. He wishes to thank the German National Academic Foundation for funding this stay and Professor Mathias Schulze for the supervision of his Bachelor thesis at the University of Kaiserslautern.
Funding Information:
Acknowledgements The first author is partially supported by JSPS Grant-in-Aid for Young Scientists (B) No. 24740012. The main part of this work was done during a research stay of the second author at Kyoto University. He wishes to thank the German National Academic Foundation for funding this stay and Professor Mathias Schulze for the supervision of his Bachelor thesis at the University of Kaiserslautern.
Publisher Copyright:
© 2017, Springer Science+Business Media, LLC, part of Springer Nature.
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.
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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 -