{
  "id": "1606.09138",
  "version": "v1",
  "published": "2016-06-29T14:56:37.000Z",
  "updated": "2016-06-29T14:56:37.000Z",
  "title": "Classical formulae on projective surfaces and $3$-folds with ordinary singularities, revisited",
  "authors": [
    "Takahisa Sasajima",
    "Toru Ohmoto"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "As an application of universal polynomials for local and multi-singularities of maps, we revisit classical formulae of Salmon-Cayley-Zeuthen for projective surfaces and analogous formulae of Segre-Severi-Roth for projective $3$-folds. In particular, several examples of actual computation are given using universal polynomials for computing weighted Euler characteristics of singularity loci.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-29T14:56:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "projective surfaces",
      "ordinary singularities",
      "universal polynomials",
      "revisit classical formulae",
      "singularity loci"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}