{
  "id": "1703.03991",
  "version": "v1",
  "published": "2017-03-11T16:16:03.000Z",
  "updated": "2017-03-11T16:16:03.000Z",
  "title": "About Chow groups of certain hyperkähler varieties with non-symplectic automorphisms",
  "authors": [
    "Robert Laterveer"
  ],
  "comment": "16 pages, to appear in Vietnam J. Math., comments welcome",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a hyperk\\\"ahler variety, and let $G$ be a group of finite order non-symplectic automorphisms of $X$. Beauville's conjectural splitting property predicts that each Chow group of $X$ should split in a finite number of pieces. The Bloch-Beilinson conjectures predict how $G$ should act on these pieces of the Chow groups: certain pieces should be invariant under $G$, while certain other pieces should not contain any non-trivial $G$-invariant cycle. We can prove this for two pieces of the Chow groups when $X$ is the Hilbert scheme of a $K3$ surface and $G$ consists of natural automorphisms. This has consequences for the Chow ring of the quotient $X/G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-11T16:16:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30"
    ],
    "keywords": [
      "chow group",
      "hyperkähler varieties",
      "finite order non-symplectic automorphisms",
      "beauvilles conjectural splitting property predicts",
      "bloch-beilinson conjectures predict"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}