{
  "id": "1611.08818",
  "version": "v1",
  "published": "2016-11-27T10:19:49.000Z",
  "updated": "2016-11-27T10:19:49.000Z",
  "title": "A remark on the motive of the Fano variety of lines of a cubic",
  "authors": [
    "Robert Laterveer"
  ],
  "comment": "12 pages,to appear in Ann. math. Quebec, comments welcome !",
  "doi": "10.1007/s40316-016-0070-x",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth cubic hypersurface, and let $F$ be the Fano variety of lines on $X$. We establish a relation between the Chow motives of $X$ and $F$. This relation implies in particular that if $X$ has finite-dimensional motive (in the sense of Kimura), then $F$ also has finite-dimensional motive. This proves finite-dimensionality for motives of Fano varieties of cubics of dimension $3$ and $5$, and of certain cubics in other dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-27T10:19:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30",
      "14J70",
      "14N25"
    ],
    "keywords": [
      "fano variety",
      "smooth cubic hypersurface",
      "finite-dimensional motive",
      "chow motives",
      "relation implies"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}