{
  "id": "2109.01043",
  "version": "v1",
  "published": "2021-09-02T16:01:29.000Z",
  "updated": "2021-09-02T16:01:29.000Z",
  "title": "Sparsity of Integral Points on Moduli Spaces of Varieties",
  "authors": [
    "Jordan S. Ellenberg",
    "Brian Lawrence",
    "Akshay Venkatesh"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $X$ be a quasi-projective variety over a number field, admitting (after passage to $\\mathbb{C}$) a geometric variation of Hodge structure whose period mapping has zero-dimensional fibers. Then the integral points of $X$ are sparse: the number of such points of height $\\leq B$ grows slower than any positive power of $B$. For example, homogeneous integral polynomials in a fixed number of variables and degree, with discriminant divisible only by a fixed set of primes, are sparse when considered up to integral linear substitutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-02T16:01:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integral points",
      "moduli spaces",
      "integral linear substitutions",
      "number field",
      "geometric variation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}