{
  "id": "1410.4142",
  "version": "v1",
  "published": "2014-10-15T17:17:32.000Z",
  "updated": "2014-10-15T17:17:32.000Z",
  "title": "Enumeration of singular hypersurfaces on arbitrary complex manifolds",
  "authors": [
    "Ritwik Mukherjee"
  ],
  "comment": "6 pages; comments are welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we obtain an explicit formula for the number of hypersurfaces in a compact complex manifold X (passing through the right number of points), that has a simple node, a cusp or a tacnode. The hypersurfaces belong to a linear system, which is obtained by considering a holomorphic line bundle L over X. 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": "2014-10-15T17:17:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N10",
      "14H20",
      "55R55",
      "57R20",
      "57R22",
      "57R45"
    ],
    "keywords": [
      "arbitrary complex manifolds",
      "singular hypersurfaces",
      "enumeration",
      "compact complex manifold",
      "generic smooth section"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4142M"
    }
  }
}