{
  "id": "2002.07733",
  "version": "v1",
  "published": "2020-02-18T17:07:15.000Z",
  "updated": "2020-02-18T17:07:15.000Z",
  "title": "The construction problem for Hodge numbers modulo an integer in positive characteristic",
  "authors": [
    "Remy van Dobben de Bruyn",
    "Matthias Paulsen"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $k$ be an algebraically closed field of positive characteristic. For any integer $m \\geq 2$, we show that the Hodge numbers of a smooth projective $k$-variety can take on any combination of values modulo $m$, subject only to Serre duality. In particular, there are no non-trivial polynomial relations between the Hodge numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-18T17:07:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F99",
      "14G17",
      "14A10",
      "14E99",
      "14F40"
    ],
    "keywords": [
      "hodge numbers modulo",
      "positive characteristic",
      "construction problem",
      "non-trivial polynomial relations",
      "serre duality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}