{
  "id": "1901.04809",
  "version": "v1",
  "published": "2019-01-15T13:28:37.000Z",
  "updated": "2019-01-15T13:28:37.000Z",
  "title": "On the Chow ring of certain hypersurfaces in a Grassmannian",
  "authors": [
    "Robert Laterveer"
  ],
  "comment": "11 pages, to appear in Le Matematiche, comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "This small note is about Pl\\\"ucker hyperplane sections $X$ of the Grassmannian $\\operatorname{Gr}(3,V_{10})$. Inspired by the analogy with cubic fourfolds, we prove that the only non-trivial Chow group of $X$ is generated by Grassmannians of type $\\operatorname{Gr}(3,W_{6})$ contained in $X$. We also prove that a certain subring of the Chow ring of $X$ (containing all intersections of positive-codimensional subvarieties) injects into cohomology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-15T13:28:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30"
    ],
    "keywords": [
      "chow ring",
      "grassmannian",
      "hypersurfaces",
      "non-trivial chow group",
      "small note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}