{
  "id": "1310.7871",
  "version": "v2",
  "published": "2013-10-29T16:41:40.000Z",
  "updated": "2015-02-12T13:22:16.000Z",
  "title": "Fibered Threefolds and Lang-Vojta's Conjecture over Function Fields",
  "authors": [
    "Amos Turchet"
  ],
  "comment": "updated version: introduction partly rewritten, section 2 partly corrected (lemma 2.1), in section 4 the computation are corrected with a light modification of the constant involved",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Using the techniques introduced by Corvaja and Zannier we solve the non-split case of the geometric Lang-Vojta Conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane. In this situation we deal with sections of an affine threefold fibered over a curve, whose boundary, in the natural projective completion, is a quartic bundle over the base whose fibers have three irreducible components. We prove that the image of each section has bounded degree in terms of the Euler Characteristic of the base curve.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-29T16:41:40.000Z",
      "abstract": "Using Corvaja and Zannier techniques in the split case for the complement of a conic and two lines in $\\mathbf{P}^{2}$, we solve Lang-Vojta's conjecture over function fields for the non-split case of complements of degree four and three component divisors in the projective plane. In this situation we deal with the case of an affine threefold fibered over a curve in which every fiber is isomorphic to the complement of a conic and two lines in the projective plane. We prove that sections of such a threefold have bounded image in terms of the Euler Characteristic of the curve.",
      "comment": "16 pages. arXiv admin note: text overlap with arXiv:math/0512074 by other authors",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-12T13:22:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G50"
    ],
    "keywords": [
      "function fields",
      "lang-vojtas conjecture",
      "fibered threefolds",
      "projective plane",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.7871T"
    }
  }
}