{
  "id": "2107.05543",
  "version": "v1",
  "published": "2021-07-12T16:11:35.000Z",
  "updated": "2021-07-12T16:11:35.000Z",
  "title": "Conics meeting eight lines over perfect fields",
  "authors": [
    "Cameron Darwin",
    "Aygul Galimova",
    "Miao Pam Gu",
    "Stephen McKean"
  ],
  "comment": "16 pages. Comments welcome!",
  "categories": [
    "math.AG"
  ],
  "abstract": "Over the complex numbers, there are 92 plane conics meeting 8 general lines in projective 3-space. Using the Euler class and local degree from motivic homotopy theory, we give an enriched version of this result over any perfect field. This provides a weighted count of the number of plane conics meeting 8 general lines, where the weight of each conic is determined the geometry of its intersections with the 8 given lines. As a corollary, real conics meeting 8 general lines come in two families of equal size.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-12T16:11:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14N15",
      "14F52"
    ],
    "keywords": [
      "perfect field",
      "plane conics meeting",
      "motivic homotopy theory",
      "general lines come",
      "euler class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}