{
  "id": "1212.0552",
  "version": "v2",
  "published": "2012-12-03T21:01:17.000Z",
  "updated": "2020-10-07T08:28:29.000Z",
  "title": "On the Chow groups of the variety of lines of a cubic fourfold",
  "authors": [
    "Mingmin Shen",
    "Charles Vial"
  ],
  "comment": "This paper was superseded by Part 3 and the appendices of arXiv:1309.5965",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a smooth complex cubic fourfold and let $F$ be the variety of lines of $X$. The variety $F$ is known to be a smooth projective hyperkaehler fourfold, which is moreover endowed with a self rational map $\\phi : F -\\rightarrow F$ first constructed by C. Voisin. Here we define a filtration of Bloch--Beilinson type on the Chow group of zero-cycles $CH_0(F)$ which canonically splits under the action of $\\phi$, thereby answering in this case a question of A. Beauville. Moreover, we show that this filtration is of motivic origin, in the sense that it arises from a Chow--Kuenneth decomposition of the diagonal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-03T21:01:17.000Z",
      "comment": "28 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2020-10-07T08:28:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14C15",
      "53C26",
      "14J28"
    ],
    "keywords": [
      "chow group",
      "smooth complex cubic fourfold",
      "self rational map",
      "smooth projective hyperkaehler fourfold",
      "filtration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.0552S"
    }
  }
}