{
  "id": "math/0302005",
  "version": "v1",
  "published": "2003-01-31T21:23:37.000Z",
  "updated": "2003-01-31T21:23:37.000Z",
  "title": "Towards Characterizing Morphisms Between High Dimensional Hypersurfaces",
  "authors": [
    "David Sheppard"
  ],
  "comment": "15 pages, first paper of graduate thesis",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that for every morphism f between nonsingular hypersurfaces of dimension at least 3 and of general type in projective space, there is an everywhere defined endomorphism F of projective space that restricts to f. As a corollary, we see that if X,Y are nonsingular hypersurfaces of general type of dimension at least 3 such that there is a nonconstant morphism f from X to Y, then degY divides degX with quotient q, and moreover the endomorphism F of projective space is given by polynomials of degree q.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-01-31T21:23:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J70",
      "14J30"
    ],
    "keywords": [
      "high dimensional hypersurfaces",
      "characterizing morphisms",
      "projective space",
      "nonsingular hypersurfaces",
      "general type"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......2005S"
    }
  }
}