{
  "id": "2105.02224",
  "version": "v1",
  "published": "2021-05-05T12:33:47.000Z",
  "updated": "2021-05-05T12:33:47.000Z",
  "title": "Algebraic cycles and intersections of a quadric and a cubic",
  "authors": [
    "Robert Laterveer"
  ],
  "comment": "14 pages, comments very welcome. arXiv admin note: substantial text overlap with arXiv:2105.02016; text overlap with arXiv:2009.11061",
  "journal": "Forum Mathematicum 33 no. 3 (2021), 845-855",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $Y$ be a smooth complete intersection of a quadric and a cubic in $\\mathbb{P}^n$, with $n$ even. We show that $Y$ has a multiplicative Chow-K\\\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of (powers of) $Y$ displays K3-like behaviour. As a by-product of the argument, we also establish a multiplicative Chow-K\\\"unneth decomposition for the resolution of singularities of a general nodal cubic hypersurface of even dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-05T12:33:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C30"
    ],
    "keywords": [
      "algebraic cycles",
      "general nodal cubic hypersurface",
      "smooth complete intersection",
      "displays k3-like behaviour",
      "decomposition"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}