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PreprintCC BY 4.0arXiv

On an exponent-preserving duality for Coxeter multiarrangements of type B2

  • Shota Maehara
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Abstract

In the theory of hyperplane arrangements, the study of logarithmic derivation modules is one of the most important subjects. If the module is free over a graded ring, the multiset of degrees of its homogeneous basis is called exponents. We utilize some basic theory of linear algebra to study the exponents of multiarrangements. As an application, we show a new exponent-preserving duality for the Coxeter multiarrangements of type B2, which was conjectured by Torsten Hoge.

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Cite

BibTeXRIS
BibTeX
@misc{maehara2026exponentpreserving,
  title = {{On an exponent-preserving duality for Coxeter multiarrangements of type $B_2$}},
  author = {Shota Maehara},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36547},
  eprint = {2610.36547},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36547},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On an exponent-preserving duality for Coxeter multiarrangements of type B_2
AU  - Shota Maehara
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36547
UR  - https://arxiv.org/abs/2610.36547
AB  - In the theory of hyperplane arrangements, the study of logarithmic derivation modules is one of the most important subjects. If the module is free over a graded ring, the multiset of degrees of its homogeneous basis is called exponents. We utilize some basic theory of linear algebra to study the exponents of multiarrangements. As an application, we show a new exponent-preserving duality for the Coxeter multiarrangements of type B_2, which was conjectured by Torsten Hoge.
ER  -