{
  "id": "1709.01698",
  "version": "v1",
  "published": "2017-09-06T07:13:01.000Z",
  "updated": "2017-09-06T07:13:01.000Z",
  "title": "The 2-Hessian and sextactic points on plane algebraic curves",
  "authors": [
    "Paul Aleksander Maugesten",
    "Torgunn Karoline Moe"
  ],
  "comment": "18 pages, 1 figure, results partially from first author's master's thesis",
  "categories": [
    "math.AG"
  ],
  "abstract": "In an article from 1865 Arthur Cayley claims that given a plane algebraic curve there exists an associated 2-Hessian curve that intersects it in its sextactic points. In this paper we fix an error in Cayley's calculations and provide the correct defining polynomial for the 2-Hessian of a plane curve. In addition, we provide a formula for the number of sextactic points on cuspidal curves and tie this formula to the 2-Hessian. Lastly, we consider the special case of rational curves, where the sextactic points can be interpreted as the zeros of the Wronski determinant of the 2nd Veronese embedding of the curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-06T07:13:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H50",
      "14H45",
      "14H20"
    ],
    "keywords": [
      "plane algebraic curve",
      "sextactic points",
      "arthur cayley claims",
      "rational curves",
      "2nd veronese"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}