{
  "id": "1903.05430",
  "version": "v1",
  "published": "2019-03-13T11:52:32.000Z",
  "updated": "2019-03-13T11:52:32.000Z",
  "title": "The construction problem for Hodge numbers modulo an integer",
  "authors": [
    "Matthias Paulsen",
    "Stefan Schreieder"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AG",
    "math.CV",
    "math.GT"
  ],
  "abstract": "For any integer $m\\ge2$ and any dimension $n\\ge1$, we show that any $n$-dimensional Hodge diamond with values in $\\mathbb Z/m\\mathbb Z$ is attained by the Hodge numbers of an $n$-dimensional smooth complex projective variety. As a corollary, there are no polynomial relations among the Hodge numbers of $n$-dimensional smooth complex projective varieties besides the ones induced by the Hodge symmetries, which answers a question raised by Koll\\'ar in 2012.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-13T11:52:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32Q15",
      "14C30",
      "14E99",
      "51M15"
    ],
    "keywords": [
      "hodge numbers modulo",
      "dimensional smooth complex projective variety",
      "construction problem",
      "dimensional hodge diamond"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}