{
  "id": "2212.01664",
  "version": "v1",
  "published": "2022-12-03T18:35:05.000Z",
  "updated": "2022-12-03T18:35:05.000Z",
  "title": "Counting rational curves with an $m$-fold point",
  "authors": [
    "Indranil Biswas",
    "Chitrabhanu Chaudhuri",
    "Apratim Choudhury",
    "Ritwik Mukherjee",
    "Anantadulal Paul"
  ],
  "comment": "22 pages, 15 figures",
  "categories": [
    "math.AG",
    "math.DG",
    "math.SG"
  ],
  "abstract": "We obtain a recursive formula for the number of rational degree $d$ curves in $\\mathbb{CP}^2$ that pass through $3d+1-m$ generic points and that have an $m$-fold singular point. The special case of counting curves with a triple point was solved earlier by other authors. We obtain the formula by considering a family version of Kontsevich's recursion formula, in contrast to the excess intersection theoretic approach of others. A large number of low degree cases have been worked out explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-03T18:35:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N35",
      "14J45",
      "53D45"
    ],
    "keywords": [
      "counting rational curves",
      "fold point",
      "excess intersection theoretic approach",
      "low degree cases",
      "fold singular point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}