{
  "id": "2109.06394",
  "version": "v1",
  "published": "2021-09-14T01:48:14.000Z",
  "updated": "2021-09-14T01:48:14.000Z",
  "title": "Dynamical Systems of Correspondences on the Projective Line I: Moduli Spaces and Multiplier Maps",
  "authors": [
    "Rin Gotou"
  ],
  "comment": "24 pages",
  "categories": [
    "math.DS",
    "math.AG"
  ],
  "abstract": "We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We obtain the rationality of the moduli spaces. The rationality of the moduli space of degree $(d,e)$ correspondences is obtained from a representation-theoretic projection to the one for the usual dynamical systems of degree $d+e-1$. We also show that the multiplier maps for the fixed points and the multiplier index theorem (Woods Hole formula) are also reduced through the projection and obtain the reduced form explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-14T01:48:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37F05",
      "12E05",
      "14C05",
      "14E08",
      "37F25",
      "37P45"
    ],
    "keywords": [
      "moduli space",
      "projective line",
      "multiplier maps",
      "correspondences",
      "woods hole formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}