Heavy hyperplanes in multiarrangements and their freeness

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.

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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.

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Correspondence to Lukas Kühne.

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Abe, T., Kühne, L. Heavy hyperplanes in multiarrangements and their freeness. J Algebr Comb 48, 581–606 (2018). https://doi.org/10.1007/s10801-017-0806-y

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Keywords

  • Hyperplane arrangements
  • Freeness
  • Multiarrangements
  • Supersolvable arrangements