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The separator-based derivations for arrangements of monomial groups
Abstract
We investigate derivation modules of hyperplane arrangements associated with the monomial groups G(r,p,ℓ). Motivated by Mühlherr's separator-based construction for graphic arrangements, we extend this approach by combining separators with integral expressions. For a subarrangement 𝒜G defined by a graph G, we show that, when p<r, the derivation module 𝒟(𝒜G) is generated by the standard derivations η0,…,ηκ(G) together with a finite set of separator-based derivations. This result generalizes the complete graph case and provides new evidence toward the broader applicability of separator methods in the study of hyperplane arrangements.
Related
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BibTeX
@misc{wang2026separatorbased,
title = {{The separator-based derivations for arrangements of monomial groups}},
author = {Zixuan Wang and Weili Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06098},
eprint = {2610.06098},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06098},
}
RIS
TY - UNPB
TI - The separator-based derivations for arrangements of monomial groups
AU - Zixuan Wang
AU - Weili Guo
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06098
UR - https://arxiv.org/abs/2610.06098
AB - We investigate derivation modules of hyperplane arrangements associated with the monomial groups G(r,p,ℓ). Motivated by Mühlherr's separator-based construction for graphic arrangements, we extend this approach by combining separators with integral expressions. For a subarrangement 𝒜_G defined by a graph G, we show that, when p<r, the derivation module 𝒟(𝒜_G) is generated by the standard derivations η_0,…,η_κ(G) together with a finite set of separator-based derivations. This result generalizes the complete graph case and provides new evidence toward the broader applicability of separator methods in the study of hyperplane arrangements.
ER -