{
  "id": "2408.07631",
  "version": "v1",
  "published": "2024-08-14T15:57:28.000Z",
  "updated": "2024-08-14T15:57:28.000Z",
  "title": "Counting rational points on Hirzebruch-Kleinschmidt varieties over global function fields",
  "authors": [
    "Sebastián Herrero",
    "Tobías Martínez",
    "Pedro Montero"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2407.19408",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Inspired by Bourqui's work on anticanonical height zeta functions on Hirzebruch surfaces, we study height zeta functions of split toric varieties with Picard rank 2 over global function fields, with respect to height functions associated with big metrized line bundles. We show that these varieties can be naturally decomposed into a finite disjoint union of subvarieties, where precise analytic properties of the corresponding height zeta functions can be given, allowing for a finer inspection of the asymptotic number of rational points of bounded height on each subvariety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-14T15:57:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G50",
      "11M41",
      "14M25",
      "11G35"
    ],
    "keywords": [
      "global function fields",
      "counting rational points",
      "hirzebruch-kleinschmidt varieties",
      "study height zeta functions",
      "corresponding height zeta functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}