{
  "id": "1812.04094",
  "version": "v1",
  "published": "2018-12-10T21:15:21.000Z",
  "updated": "2018-12-10T21:15:21.000Z",
  "title": "Indeterminacy loci of iterate maps in moduli space",
  "authors": [
    "Jan Kiwi",
    "Hongming Nie"
  ],
  "comment": "34 pages, 2 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "The moduli space $\\mathrm{rat}_d$ of rational maps in one complex variable of degree $d \\ge 2$ has a natural compactification by a projective variety $\\overline{\\mathrm{rat}}_d$ provided by geometric invariant theory. Given $n \\ge 2$, the iteration map $\\Phi_n : \\mathrm{rat}_d \\to\\mathrm{rat}_{d^n}$, defined by $\\Phi_n: [f] \\mapsto [f^n]$, extends to a rational map $\\Phi_n : \\overline{\\mathrm{rat}}_d\\dashrightarrow \\overline{\\mathrm{rat}}_{d^n}$. We characterize the elements of $\\overline{\\mathrm{rat}}_d$ which lie in the indeterminacy locus of $\\Phi_n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-10T21:15:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moduli space",
      "indeterminacy locus",
      "iterate maps",
      "rational map",
      "geometric invariant theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}