{
  "id": "math/0611715",
  "version": "v3",
  "published": "2006-11-23T07:43:12.000Z",
  "updated": "2016-01-26T11:03:26.000Z",
  "title": "Diophantine Approximation on projective Varieties I: Algebraic distance and metric Bézout Theorem",
  "authors": [
    "Heinrich Massold"
  ],
  "comment": "53 pages, One major error (proof of old Proposition 4.16.3) corrected, Calculus slightly simplified",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "For two properly intersecting effective cycles in projective space X,Y, and their intersection product Z, the metric Bezout Theorem relates the degrees, heights of X,Y, and Z, as well as their distances and algebraic distances to a given point theta. Applications of this Theorem are in the area of Diophantine Approximation, giving estimates for approximation properties of Z with respect to $\\theta$ against the ones of X, and Y.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-11-26T19:05:15.000Z",
      "abstract": "Apart from the well known algebraic and arithmetic B\\'ezout Theorems, there also is the metric B\\'ezout Theorem. For two properly intersecting effective cycles in projective space X,Y, and their intersection product Z, it relates not only the degrees and heights of X,Y, and Z, but also their distances and algebraic distances to a given point $\\theta$. Applications of this Theorem will lie in the area of Diophantine Approximation, where one wants to estimate approximation properties of Z with respect to $\\theta$ against the ones of X, and Y.",
      "comment": "46 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-01-26T11:03:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40",
      "14G25",
      "11G35",
      "11J83",
      "11J13"
    ],
    "keywords": [
      "metric bézout theorem",
      "algebraic distance",
      "diophantine approximation",
      "projective varieties",
      "arithmetic bezout theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 53,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11715M"
    }
  }
}