{
  "id": "math/0201225",
  "version": "v1",
  "published": "2002-01-23T16:37:34.000Z",
  "updated": "2002-01-23T16:37:34.000Z",
  "title": "Nodal curves and Riccati solutions of Painlevé equations",
  "authors": [
    "Masa-Hiko Saito",
    "Hitomi Terajima"
  ],
  "comment": "30 pages, 4 figures",
  "journal": "J. Math. Kyoto Univ., 44(2004), no.3, 529--568",
  "categories": [
    "math.AG",
    "math.QA"
  ],
  "abstract": "In this paper, we study Riccati solutions of Painlev\\'e equations from a view point of geometry of Okamoto-Painlev\\'e pairs $(S,Y)$. After establishing the correspondence between (rational) nodal curves on $S-Y$ and Riccati solutions, we give the complete classification of the configurations of nodal curves on $S-Y$ for each Okamoto-Painlev\\'e pair $(S, Y)$. As an application of the classification, we prove the non-existence of Riccati solutions of Painlev\\'e equations of types $P_{I}, P_{III}^{\\tilde{D}_8}$ and $P_{III}^{\\tilde{D}_7}$. We will also give a partial answer to the conjecture in (STT) and (T) that the dimension of the local cohomology $H^1_{Y_{red}}(S,\\Theta_S(-\\log Y_{red}))$ is one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-01-23T16:37:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14D15",
      "34M55",
      "32G10"
    ],
    "keywords": [
      "nodal curves",
      "painleve equations",
      "okamoto-painleve pair",
      "study riccati solutions",
      "view point"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1225S"
    }
  }
}