{
  "id": "math/0701353",
  "version": "v1",
  "published": "2007-01-12T17:26:38.000Z",
  "updated": "2007-01-12T17:26:38.000Z",
  "title": "Andreotti-Mayer loci and the Schottky problem",
  "authors": [
    "Ciro Ciliberto",
    "Gerard van der Geer"
  ],
  "comment": "46 pages, Latex",
  "categories": [
    "math.AG"
  ],
  "abstract": "We prove a lower bound for the codimension of the Andreotti-Mayer locus N_{g,1} and show that the lower bound is reached only for the hyperelliptic locus in genus 4 and the Jacobian locus in genus 5. In relation with the boundary of the Andreotti-Mayer loci we study subvarieties of principally polarized abelian varieties (B,Theta) parametrizing points b such that Theta and the translate Theta_b are tangentially degenerate along a variety of a given dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-12T17:26:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "andreotti-mayer locus",
      "schottky problem",
      "lower bound",
      "hyperelliptic locus",
      "jacobian locus"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1353C"
    }
  }
}