{
  "id": "0906.4152",
  "version": "v5",
  "published": "2009-06-23T01:50:20.000Z",
  "updated": "2015-03-22T03:07:30.000Z",
  "title": "Topology of Blow-ups and Enumerative Geometry",
  "authors": [
    "Haibao Duan",
    "Banghe Li"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG",
    "math.AT"
  ],
  "abstract": "Let M be the blow--up of a manifold M along a submanifold X. In this paper we present closed formulae for the integral cohomology and the total Chern class of M. As applications we compute the cohomology of the varieties of complete conics and complete quadrices in 3--space, and justify two enumerative results due to Schubert.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-10-26T00:44:19.000Z",
      "abstract": "Let M be the blow-up of a complex manifold along a submanifold. We determine the integral cohomology ring and obtain a formula for the Chern classes of M. As applications we determine the cohomology rings for the varieties of complete conics and complete quadrices in 3-space, and justify two enumerative results due to Schubert [S1].",
      "comment": "19 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v5",
      "updated": "2015-03-22T03:07:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "14M15"
    ],
    "keywords": [
      "enumerative geometry",
      "complete quadrices",
      "complex manifold",
      "complete conics",
      "integral cohomology ring"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.4152D"
    }
  }
}