{
  "id": "1501.01557",
  "version": "v1",
  "published": "2015-01-07T16:52:02.000Z",
  "updated": "2015-01-07T16:52:02.000Z",
  "title": "Counting curves on a general linear system with up to two singular points",
  "authors": [
    "Somnath Basu",
    "Ritwik Mukherjee"
  ],
  "comment": "22 pages; generalizes results of our previous papers to curves on any linear system. We welcome comments and suggestions",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "In this paper we obtain an explicit formula for the number of curves in a compact complex surface $X$ (passing through the right number of generic points), that has up to one node and one singularity of codimension $k$, provided the total codimension is at most $7$. We use a classical fact from differential topology: the number of zeros of a generic smooth section of a vector bundle $V$ over $M$, counted with signs, is the Euler class of $V$ evaluated on the fundamental class of $M$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-07T16:52:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14H20",
      "55R55",
      "57R20",
      "57R22",
      "57R45"
    ],
    "keywords": [
      "general linear system",
      "singular points",
      "counting curves",
      "compact complex surface",
      "generic smooth section"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150101557B"
    }
  }
}