{
  "id": "2411.08006",
  "version": "v1",
  "published": "2024-11-12T18:30:29.000Z",
  "updated": "2024-11-12T18:30:29.000Z",
  "title": "On the FOD/FOM parameter of rational maps",
  "authors": [
    "Ruben A. Hidalgo"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "Let $\\chi$ be a (right) action of ${\\rm PSL}_{2}({\\mathbb L})$ on the space ${\\mathbb L}(z)$ of rational maps defined over an algebraically closed field ${\\mathbb L}$. If $R \\in {\\mathbb L}(z)$ and ${\\mathcal M}_{R}^{\\chi}$ is its $\\chi$-field of moduli, then the parameter ${\\rm FOD/FOM}_{\\chi}(R)$ is the smallest integer $n \\geq 1$ such that there is a $\\chi$-field of definition of $R$ being a degree $n$ extension of ${\\mathcal M}_{R}^{\\chi}$. When ${\\mathbb L}$ has characteristic zero and $\\chi=\\chi_{\\infty}$ is the conjugation action, then it is known that ${\\rm FOD/FOM}_{\\chi_{\\infty}}(R) \\leq 2$. In this paper, we study the above parameter for general actions and any characteristic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-12T18:30:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F10",
      "37P05",
      "30F30"
    ],
    "keywords": [
      "rational maps",
      "fod/fom parameter",
      "characteristic zero",
      "conjugation action",
      "general actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}