{
  "abstract": "This paper provides methods to compute degrees of Fano quiver moduli and gives explicit degree formulas for two classes of them. One such class is a series of toric Fano varieties that parametrize isomorphism classes of representations of the bipartite quiver $K_{(2,q)}^m$ with dimension vector $\\underline{1}$, and the other class is the moduli space of q-point configurations on $\\mathbb{P}^1$. In the former case, we obtain a formula comprised of sums of binomial coefficients in $q$ and $m$. Its special case $m = 1$ turns out to be the same as the central MacMahon numbers (OEIS entry A177043). In the latter case, we obtained a formula over $\\mathbb{Q}$. These formulas are much more efficient than computing directly in Chow rings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13599",
  "author_total": 1,
  "authors": [
    {
      "name": "Pengcheng Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5n9fvj4fe49r3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13599",
  "fulltext_url": null,
  "id": "5n9fvj4fe49r3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13599",
  "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"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213245287",
  "pdf_url": "https://arxiv.org/pdf/2609.13599",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5n9fvj4fe49r3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13599",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13599"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Degrees of Fano Quiver Moduli",
  "title_text": "Degrees of Fano Quiver Moduli",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5n9fvj4fe49r3",
  "venue": "arXiv",
  "versions": []
}