{
  "abstract": "We prove a criteria for the Behrend function values on the Hilbert scheme of $n$-points on $\\C^3$ from local monodromy and the Denef--Loeser's Lefschetz trace formula of jet spaces. If the power two, three, or four of the monodromy is unipotent, it reduces respectively to a Hessian parity formula, a cubic-complement formula, or a quartic formula. This gives a Milnor fiber and monodromy based proof of nonconstancy of the Behrend function on $\\Hilb^n(\\C^3)$ after Jelisiejew-Kool-Schmiermann. We also calculate two ideals in $\\Hilb^9(\\C^3)$ and $\\Hilb^{12}(\\C^3)$ so that the Behrend function is not $\\pm 1$, answering a question of Ricolfi.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22469",
  "author_total": 1,
  "authors": [
    {
      "name": "Yunfeng Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d1t5yfb24b22m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22469",
  "fulltext_url": null,
  "id": "d1t5yfb24b22m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22469",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214030506",
  "pdf_url": "https://arxiv.org/pdf/2609.22469",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d1t5yfb24b22m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.22469",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22469"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Local monodromy, Behrend function and Hilbert scheme of points on $\\mathbb{C}^3$",
  "title_text": "Local monodromy, Behrend function and Hilbert scheme of points on ℂ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/d1t5yfb24b22m",
  "venue": "arXiv",
  "versions": []
}