{
  "id": "0907.3293",
  "version": "v6",
  "published": "2009-07-20T12:04:30.000Z",
  "updated": "2011-10-05T14:57:48.000Z",
  "title": "Geometry of the Discriminant Surface for Quadratic Forms",
  "authors": [
    "Sergei D. Mechveliani"
  ],
  "comment": "26 pages. Cites 9 references. A draft paper. Withdraw earlier versions. Changes since 2009: 1) computer algebra part removed, 2) results from Arnold's book referenced, 3) many points canceled, many points improved",
  "categories": [
    "math.AG"
  ],
  "abstract": "We investigate the manifold $\\cal{M}$ of (real) quadratic forms in n > 1 variables having a multiple eigenvalue. In addition to known facts, we prove that 1) $\\cal{M}$ is irreducible, 2) in the case of n = 3, scalar matrices and only them are singular points on $\\cal{M}$. For $n = 3$, $\\cal{M}$ is also described as the straight cylinder over $\\cal{M}$$_0$, where $\\cal{M}$$_0$ is the cone over the orbit of the diagonal matrix $\\diag(1,1,-2)$ by the orthogonal changes of coordinates. We analyze certain properties of this orbit, which occurs a diffeomorphic image of the projective plane.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2011-10-05T14:57:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quadratic forms",
      "discriminant surface",
      "scalar matrices",
      "diffeomorphic image",
      "singular points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0907.3293M"
    }
  }
}