{
  "id": "1810.08566",
  "version": "v1",
  "published": "2018-10-19T16:04:14.000Z",
  "updated": "2018-10-19T16:04:14.000Z",
  "title": "Differential Galois theory and isomonodromic deformations",
  "authors": [
    "David Blázquez-Sanz",
    "Guy Casale",
    "Juan Sebastián Díaz Arboleda"
  ],
  "comment": "28 pages",
  "categories": [
    "math.CA",
    "math.DG"
  ],
  "abstract": "Here we present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois group with parameters of a connection with simple $G$ is determined by its isomonodromic deformations. This allows us to compute the Galois groups with parameters of the general Fuchsian special linear system and of Gauss hypergeometric equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T16:04:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C05",
      "14L30",
      "12H05"
    ],
    "keywords": [
      "differential galois theory",
      "isomonodromic deformations",
      "general fuchsian special linear system",
      "galois group",
      "parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}