{
  "id": "2108.09949",
  "version": "v1",
  "published": "2021-08-23T05:45:10.000Z",
  "updated": "2021-08-23T05:45:10.000Z",
  "title": "One numerical obstruction for rational maps between hypersurfaces",
  "authors": [
    "Ilya Karzhemanov"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Given a rational dominant map $\\phi: Y \\dashrightarrow X$ between two generic hypersurfaces $Y,X \\subset \\mathbb{P}^n$ of dimension $\\ge 3$, we prove (under an addition assumption on $\\phi$) a ``Noether--Fano type'' inequality $m_Y \\ge m_X$ for certain (effectively computed) numerical invariants of $Y$ and $X$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-23T05:45:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational maps",
      "numerical obstruction",
      "rational dominant map",
      "generic hypersurfaces",
      "addition assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}