{
  "id": "2409.12834",
  "version": "v1",
  "published": "2024-09-19T15:14:44.000Z",
  "updated": "2024-09-19T15:14:44.000Z",
  "title": "On the rationality problem for hypersurfaces",
  "authors": [
    "Jan Lange",
    "Stefan Schreieder"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We show that a very general hypersurface of degree d at least 4 and dimension at most $(d+1)2^{d-4}$ over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor $\\mathbb{A}^1$-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-19T15:14:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J70",
      "14E08",
      "14M20",
      "14C25"
    ],
    "keywords": [
      "rationality problem",
      "slightly weaker degree bound",
      "similar results hold",
      "second named author",
      "retract rational"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}