{
  "id": "1409.6702",
  "version": "v1",
  "published": "2014-09-23T19:16:00.000Z",
  "updated": "2014-09-23T19:16:00.000Z",
  "title": "Enumeration of curves with two singular points",
  "authors": [
    "Somnath Basu",
    "Ritwik Mukherjee"
  ],
  "comment": "56 pages, 1 figure; comments are welcome. arXiv admin note: text overlap with arXiv:1308.2902",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "In this paper we obtain an explicit formula for the number of curves in two dimensional complex projective space, of degree d, passing through d(d+3)/2-(k+1) generic points and having one node and one codimension k singularity, where k is at most 6. Our main tool is a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle V over M, counted with a sign, is the Euler class of V evaluated on the fundamental class of M.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-23T19:16:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14H20",
      "55R55",
      "57R20",
      "57R22",
      "57R45"
    ],
    "keywords": [
      "singular points",
      "enumeration",
      "generic smooth section",
      "dimensional complex projective space",
      "explicit formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6702B"
    }
  }
}