{
  "id": "1410.4813",
  "version": "v1",
  "published": "2014-10-17T18:21:17.000Z",
  "updated": "2014-10-17T18:21:17.000Z",
  "title": "Schottky via the punctual Hilbert scheme",
  "authors": [
    "Martin G. Gulbrandsen",
    "Martí Lahoz"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that a smooth projective curve of genus $g$ can be reconstructed from its polarized Jacobian $(X, \\Theta)$ as a certain locus in the Hilbert scheme $\\mathrm{Hilb}^d(X)$, for $d=3$ and for $d=g+2$, defined by geometric conditions in terms of the polarization $\\Theta$. The result is an application of the Gunning--Welters trisecant criterion and the Castelnuovo--Schottky theorem by Pareschi--Popa and Grushevsky, and its scheme theoretic extension by the authors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-17T18:21:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H42",
      "14C05"
    ],
    "keywords": [
      "punctual hilbert scheme",
      "gunning-welters trisecant criterion",
      "scheme theoretic extension",
      "geometric conditions",
      "smooth projective curve"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.4813G"
    }
  }
}