{
  "id": "1307.7438",
  "version": "v2",
  "published": "2013-07-29T02:01:37.000Z",
  "updated": "2014-12-24T06:27:42.000Z",
  "title": "Linear differential equations on the Riemann sphere and representations of quivers",
  "authors": [
    "Kazuki Hiroe"
  ],
  "comment": "55 pages, some errors and typos are corrected, a section about moduli spaces of meromorphic connections is add",
  "categories": [
    "math.CA",
    "math.RT"
  ],
  "abstract": "Our interest in this paper is a generalization of the additive Deligne-Simpson problem which is originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend this problem to differential equations having an arbitrary number of unramified irregular singular points and determine the existence of solutions of the generalized additive Deligne-Simpson problems. Moreover we apply this result to the geometry of the moduli spaces of stable meromorphic connections of trivial bundles on the Riemann sphere. Namely, open embedding of the moduli spaces into quiver varieties is given and the non-emptiness condition of the moduli spaces is determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-29T02:01:37.000Z",
      "abstract": "Our interest in this paper is a generalization of additive Deligne-Simpson problems which are originally defined for Fuchsian differential equations on the Riemann sphere. We shall extend these problems to differential equations having an arbitrary number of unramified irregular singular points with poles of any order and discuss the existence of solutions of the generalized additive Deligne-Simpson problems.",
      "comment": "53pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-24T06:27:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear differential equations",
      "riemann sphere",
      "representations",
      "unramified irregular singular points",
      "fuchsian differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.7438H"
    }
  }
}