{
  "id": "0708.1229",
  "version": "v5",
  "published": "2007-08-09T09:05:11.000Z",
  "updated": "2010-01-18T07:39:49.000Z",
  "title": "On the enumeration of complex plane curves with two singular points",
  "authors": [
    "Dmitry Kerner"
  ],
  "comment": "24 pages, the Mathematica file with explicit calculations is attached. Some typos removed. To appear in the International Mathematics Research Notices",
  "journal": "International Mathematics Research Notices, 2010",
  "doi": "10.1093/imrn/rnq057",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study equi-singular strata of plane curves with two singular points of prescribed types. The method of the previous work [Kerner06] is generalized to this case. In particular we consider the enumerative problem for plane curves with two singular points of linear singularity types. First the problem for two ordinary multiple points of fixed multiplicities is solved. Then the enumeration for arbitrary linear types is reduced to the case of ordinary multiple points and to the understanding of \"merging\" of singular points. Many examples and numerical answers are given.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-01-18T07:39:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14N35",
      "14H10",
      "14H50"
    ],
    "keywords": [
      "singular points",
      "complex plane curves",
      "ordinary multiple points",
      "enumeration",
      "linear singularity types"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1229K"
    }
  }
}