Monodromy Eigenvalues of Milnor Fibers for Line Arrangements

@misc{xie2026monodromy,
  title = {{Monodromy Eigenvalues of Milnor Fibers for Line Arrangements}},
  author = {Baiting Xie and Chenglong Yu and Zhiwei Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.06416},
  eprint = {2609.06416},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.06416},
}

TY  - UNPB
TI  - Monodromy Eigenvalues of Milnor Fibers for Line Arrangements
AU  - Baiting Xie
AU  - Chenglong Yu
AU  - Zhiwei Zheng
PY  - 2026
DA  - 2026/09/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.06416
UR  - https://arxiv.org/abs/2609.06416
AB  - It is an important problem to know whether the monodromy on the cohomology of Milnor fibers associated to hyperplane arrangements is a combinatorial invariant. In this paper, we obtain a combinatorial vanishing criterion for certain eigenspaces of this algebraic monodromy in line arrangements. Combining with Hirzebruch inequality, which is a consequence of Bogomolov--Miyaoka--Yau inequality, we prove that for essential complex line arrangements, the eigenvalues of the monodromy have orders at most five. This is a partial progress toward Papadima--Suciu conjecture and proves Salvetti--Serventi connectivity conjecture. For essential complexified real line arrangements, the monodromy order is improved to at most four thanks to Shnurnikov's inequality. This confirms Papadima--Suciu conjecture for real line arrangements and also Yoshinaga's sharp pair conjecture.
ER  -