{
  "id": "0903.2005",
  "version": "v1",
  "published": "2009-03-11T16:45:49.000Z",
  "updated": "2009-03-11T16:45:49.000Z",
  "title": "Star points on smooth hypersurfaces",
  "authors": [
    "Filip Cools",
    "Marc Coppens"
  ],
  "comment": "30 pages, 1 figure",
  "categories": [
    "math.AG"
  ],
  "abstract": "A point P on a smooth hypersurface X of degree d in an N-dimensional projective space is called a star point if and only if the intersection of X with the embedded tangent space T_P(X) is a cone with vertex P. This notion is a generalization of total inflection points on plane curves and Eckardt points on smooth cubic surfaces in three-dimensional projective space. We generalize results on the configuration space of total inflection points on plane curves to star points. We give a detailed description of the configuration space for hypersurfaces with two or three star points. We investigate collinear star points and we prove that the number of star points on a smooth hypersurface is finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-11T16:45:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J70",
      "14N15",
      "14N20"
    ],
    "keywords": [
      "smooth hypersurface",
      "total inflection points",
      "configuration space",
      "plane curves",
      "collinear star points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.2005C"
    }
  }
}