{
  "id": "math/9911071",
  "version": "v1",
  "published": "1999-11-10T22:28:24.000Z",
  "updated": "1999-11-10T22:28:24.000Z",
  "title": "Autoduality of the compactified Jacobian",
  "authors": [
    "Eduardo Esteves",
    "Mathieu Gagne",
    "Steven Kleiman"
  ],
  "comment": "Plain TeX, 21 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove the following autoduality theorem for an integral projective curve C in any characteristic. Given an invertible sheaf L of degree 1, form the corresponding Abel map A_L: C->J, which maps C into its compactified Jacobian, and form its pullback map A_L^*: Pic^0_J to J, which carries the connected component of 0 in the Picard scheme back to the Jacobian. If C has, at worst, points of multiplicity 2, then A_L^* is an isomorphism, and forming it commutes with specializing C. Much of our work is valid, more generally, for a family of curves with, at worst, points of embedding dimension 2. In this case, we use the determinant of cohomology to construct a right inverse to A_L^*. Then we prove a scheme-theoretic version of the theorem of the cube, generalizing Mumford's, and use it to prove that A_L^* is independent of the choice of L. Finally, we prove our autoduality theorem: we use the presentation scheme to achieve an induction on the difference between the arithmetic and geometric genera; here, we use a few special properties of points of multiplicity 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-10T22:28:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14K30",
      "14H20"
    ],
    "keywords": [
      "compactified jacobian",
      "autoduality theorem",
      "integral projective curve",
      "picard scheme",
      "special properties"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11071E"
    }
  }
}