{
  "abstract": "Let $G$ be a finite group admitting a rational fixed-point-free (FPF) representation $V$, with a $G$-invariant full-rank lattice $L\\subset V$. We study the induced $G$-action on the complex torus $V_{\\mathbb{C}}/L$ and the quotient orbifold $V_{\\mathbb{C}}/(G\\ltimes L)$. We prove that every FPF group admits a unique irreducible rational FPF representation. We derive closed-form formulas for three core geometric invariants: the number of non-free points of the torus action, the number of singular points of the quotient orbifold, and its orbifold Euler characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27736",
  "author_total": 1,
  "authors": [
    {
      "name": "Xue Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4nbzsvq7fvtrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27736",
  "fulltext_url": null,
  "id": "4nbzsvq7fvtrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27736",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214236974",
  "pdf_url": "https://arxiv.org/pdf/2609.27736",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4nbzsvq7fvtrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27736",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27736"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Counting Invariants for Torus Quotients under FPF Group Actions",
  "title_text": "Counting Invariants for Torus Quotients under FPF Group Actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/4nbzsvq7fvtrq",
  "venue": "arXiv",
  "versions": []
}