{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06416",
  "author_total": 3,
  "authors": [
    {
      "name": "Baiting Xie"
    },
    {
      "name": "Chenglong Yu"
    },
    {
      "name": "Zhiwei Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7sgz9sztg3kns.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06416",
  "fulltext_url": null,
  "id": "7sgz9sztg3kns",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06416",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7212016686",
  "pdf_url": "https://arxiv.org/pdf/2609.06416",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7sgz9sztg3kns.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06416",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06416"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Monodromy Eigenvalues of Milnor Fibers for Line Arrangements",
  "title_text": "Monodromy Eigenvalues of Milnor Fibers for Line Arrangements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/7sgz9sztg3kns",
  "venue": "arXiv",
  "versions": []
}