{
  "id": "2003.08795",
  "version": "v1",
  "published": "2020-03-19T14:11:55.000Z",
  "updated": "2020-03-19T14:11:55.000Z",
  "title": "On Fano schemes of linear spaces of general complete intersections",
  "authors": [
    "F. Bastianelli",
    "C. Ciliberto",
    "F. Flamini",
    "P. Supino"
  ],
  "comment": "4 pages, submitted pre-print. The authors thank Lawrence Ein for having ponited out the paper of Riedl and Yang [7] in our References",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the Fano scheme $F_k(X)$ of $k$--dimensional linear subspaces contained in a complete intersection $X \\subset \\mathbb{P}^n$ of multi--degree $\\underline{d} = (d_1, \\ldots, d_s)$. Our main result is an extension of a result of Riedl and Yang concerning Fano schemes of lines on very general hypersurfaces: we consider the case when $X$ is a very general complete intersection and $\\Pi_{i=1}^s d_i > 2$ and we find conditions on $n$, $\\underline{d}$ and $k$ under which $F_k(X)$ does not contain either rational or elliptic curves. At the end of the paper, we study the case $\\Pi_{i=1}^s d_i = 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-19T14:11:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M10",
      "14C05",
      "14M15",
      "14M20"
    ],
    "keywords": [
      "general complete intersection",
      "linear spaces",
      "dimensional linear subspaces",
      "yang concerning fano schemes",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}