{
  "id": "math/9912070",
  "version": "v3",
  "published": "1999-12-09T08:54:49.000Z",
  "updated": "2000-09-14T21:19:22.000Z",
  "title": "On a compactification of the moduli space of the rational normal curves",
  "authors": [
    "Paolo Cascini"
  ],
  "comment": "15 pages, ams-latex",
  "categories": [
    "math.AG"
  ],
  "abstract": "For any odd $n$, we describe a smooth minimal (i.e. obtained by adding an irreducible hypersurface) compactification $\\tilde S_n$ of the quasi-projective homogeneous variety $S_{n}=PGL(n+1)/SL(2)$ that parameterizes the rational normal curves in $P^n$. We show that $\\tilde S_{n}$ is isomorphic to a component of the Maruyama scheme of the semi-stable sheaves on $P^n$ of rank $n$ and Chern polynomial $(1+t)^{n+2}$ and we compute its Betti numbers. In particular $\\tilde S_{3}$ is isomorphic to the variety of nets of quadrics defining twisted cubics, studied by G. Ellinsgrud, R. Piene and S. Str{\\o}mme (Space curves, Proc. Conf., LNM 1266).",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-09-14T21:19:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F05"
    ],
    "keywords": [
      "rational normal curves",
      "moduli space",
      "compactification",
      "smooth minimal",
      "isomorphic"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12070C"
    }
  }
}