{
  "id": "2405.12620",
  "version": "v1",
  "published": "2024-05-21T09:19:12.000Z",
  "updated": "2024-05-21T09:19:12.000Z",
  "title": "On the smoothability problem with rational coefficients",
  "authors": [
    "Olivier Benoist",
    "Claire Voisin"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the problem of smoothing algebraic cycles with rational coefficients on smooth projective complex varieties up to homological equivalence. We show that a solution to this problem would be incompatible with the validity of the Hartshorne conjecture on complete intersections in projective space. We also solve unconditionally a symplectic variant of this problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-21T09:19:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14J60"
    ],
    "keywords": [
      "rational coefficients",
      "smoothability problem",
      "smooth projective complex varieties",
      "smoothing algebraic cycles",
      "complete intersections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}