{
  "id": "1404.0171",
  "version": "v2",
  "published": "2014-04-01T09:21:26.000Z",
  "updated": "2014-10-17T17:29:21.000Z",
  "title": "Finite-dimensionality and cycles on powers of K3 surfaces",
  "authors": [
    "Qizheng Yin"
  ],
  "comment": "7 pages. Section 2.6 rewritten, typos fixed and further references added",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is injective. We prove that Voisin's conjecture is equivalent to the finite-dimensionality of S in the sense of Kimura-O'Sullivan. As a consequence, we obtain examples of S whose Hilbert schemes satisfy the Beauville-Voisin conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-01T09:21:26.000Z",
      "title": "Finite dimensionality and cycles on powers of K3 surfaces",
      "abstract": "For a K3 surface S, consider the subring of CH(S^n) generated by divisor and diagonal classes (with Q-coefficients). Voisin conjectures that the restriction of the cycle class map to this ring is injective. We prove that Voisin's conjecture is equivalent to the finite dimensionality of S in the sense of Kimura-O'Sullivan. As a consequence, we obtain examples of S whose Hilbert schemes satisfy the Beauville-Voisin conjecture.",
      "comment": "6 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-17T17:29:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14J28"
    ],
    "keywords": [
      "finite dimensionality",
      "k3 surface",
      "hilbert schemes satisfy",
      "cycle class map",
      "voisin conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.0171Y"
    }
  }
}