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Equivalence of freeness and higher order freeness of hyperplane arrangements

  • Takuro Abe
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Abstract

Using vector bundle theory, we prove that an essential hyperplane arrangement in an ℓ-dimensional vector space over a field of characteristic zero is free if and only if its module of logarithmic derivations of order p is free for some 1≤ p≤ℓ−1. The same statement holds for multiarrangements.

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Cite

BibTeXRIS
BibTeX
@misc{abe2026equivalence,
  title = {{Equivalence of freeness and higher order freeness of hyperplane arrangements}},
  author = {Takuro Abe},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.38550},
  eprint = {2610.38550},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.38550},
}
RIS
TY  - UNPB
TI  - Equivalence of freeness and higher order freeness of hyperplane arrangements
AU  - Takuro Abe
PY  - 2026
DA  - 2026/10/28
PB  - arXiv
DO  - 10.48550/arxiv.2610.38550
UR  - https://arxiv.org/abs/2610.38550
AB  - Using vector bundle theory, we prove that an essential hyperplane arrangement in an ℓ-dimensional vector space over a field of characteristic zero is free if and only if its module of logarithmic derivations of order p is free for some 1≤ p≤ℓ−1. The same statement holds for multiarrangements.
ER  -