{
  "id": "0809.1482",
  "version": "v3",
  "published": "2008-09-09T04:38:42.000Z",
  "updated": "2008-10-31T07:31:13.000Z",
  "title": "On Algebraic Solutions to Painleve VI",
  "authors": [
    "Katsunori Iwasaki"
  ],
  "comment": "16 pages, 9 figures, 1 table. A contribution to the Proceedings of the Conference on Exact WKB Analysis and Microlocal Analysis in RIMS, Kyoto, May, 2008",
  "categories": [
    "math.CA",
    "math.AG"
  ],
  "abstract": "We announce some results which might bring a new insight into the classification of algebraic solutions to the sixth Painleve equation. The main results consist of the rationality of parameters, trigonometric Diophantine conditions, and what the author calls the Tetrahedral Theorem regarding the absence of algebraic solutions in certain situations. The method is based on fruitful interactions between the moduli theoretical formulation of Painleve VI and dynamics on character varieties via the Riemann-Hilbert correspondence.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-10-31T07:31:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34M55",
      "32M17"
    ],
    "keywords": [
      "algebraic solutions",
      "painleve vi",
      "trigonometric diophantine conditions",
      "sixth painleve equation",
      "main results consist"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.1482I"
    }
  }
}