{
  "id": "1712.05983",
  "version": "v1",
  "published": "2017-12-16T16:11:45.000Z",
  "updated": "2017-12-16T16:11:45.000Z",
  "title": "Algebraic cycles and EPW cubes",
  "authors": [
    "Robert Laterveer"
  ],
  "comment": "32 pages, to appear in Math. Nachrichten, feedback welcome",
  "doi": "10.1002/mana.201600518",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $X$ be a hyperk\\\"ahler variety with an anti-symplectic involution $\\iota$. According to Beauville's conjectural \"splitting property\", the Chow groups of $X$ should split in a finite number of pieces such that the Chow ring has a bigrading. The Bloch-Beilinson conjectures predict how $\\iota$ should act on certain of these pieces of the Chow groups. We verify part of this conjecture for a $19$-dimensional family of hyperk\\\"ahler sixfolds that are \"double EPW cubes\" (in the sense of Iliev-Kapustka-Kapustka-Ranestad). This has interesting consequences for the Chow ring of the quotient $X/\\iota$, which is an \"EPW cube\" (in the sense of Iliev-Kapustka-Kapustka-Ranestad).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-16T16:11:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30"
    ],
    "keywords": [
      "algebraic cycles",
      "chow groups",
      "bloch-beilinson conjectures predict",
      "iliev-kapustka-kapustka-ranestad",
      "double epw cubes"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}