{
  "id": "1908.06894",
  "version": "v1",
  "published": "2019-08-19T15:52:53.000Z",
  "updated": "2019-08-19T15:52:53.000Z",
  "title": "Dominant rational maps from a very general hypersurface in the projective space",
  "authors": [
    "Yongnam Lee",
    "De-Qi Zhang"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we study dominant rational maps from a very general hypersurface $X$ of degree at least $n+3$ in the projective $(n+1)$-space ${\\mathbb P}^{n+1}$ to smooth projective $n$-folds $Y$. Based on Lefschetz theory, Hodge theory, and Cayley-Bacharach property, we prove that there is no dominant rational map from $X$ to $Y$ unless $Y$ is uniruled if the degree of the map is a prime number. Furthermore, we prove that $Y$ is rationally connected when $n=3$ and the degree of the map is a prime number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T15:52:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E05",
      "14J30",
      "14J70"
    ],
    "keywords": [
      "general hypersurface",
      "projective space",
      "study dominant rational maps",
      "prime number",
      "lefschetz theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}