{
  "abstract": "We study Chow-quotient compactifications of the moduli space of degree-$d$ rational self-maps of the projective line. We compute the degree of every three-dimensional orbit cycle in the Clebsch--Gordan compactification in terms of the main component and the hole depths. As consequences, we obtain the generic orbit class and a rational map on Chow quotients induced by iteration. We also introduce a marked Chow quotient designed to record collections of rescaling limits, describe it by decorated trees, and extend the fixed-point multiplier map to the normalization of the unmarked Chow quotient.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07668",
  "author_total": 1,
  "authors": [
    {
      "name": "Rin Gotou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/646anzbs0pb6a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07668",
  "fulltext_url": null,
  "id": "646anzbs0pb6a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07668",
  "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"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7211999661",
  "pdf_url": "https://arxiv.org/pdf/2609.07668",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/646anzbs0pb6a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07668",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07668"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits",
  "title_text": "Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/646anzbs0pb6a",
  "venue": "arXiv",
  "versions": []
}