{
  "id": "math/0005163",
  "version": "v3",
  "published": "2000-05-16T21:58:45.000Z",
  "updated": "2000-06-06T21:25:44.000Z",
  "title": "Dequantization of real algebraic geometry on logarithmic paper",
  "authors": [
    "Oleg Viro"
  ],
  "comment": "12 pages, 3 figures, Plenary talk at the 3rd ECM, Barcelona, July 10-14, 2000. Sections 2.2, 3.3, 3.4 changed, 2.3 removed to correct consequences of a miscalculation, a reference updated",
  "categories": [
    "math.AG"
  ],
  "abstract": "On logarithmic paper some real algebraic curves look like smoothed broken lines. Moreover, the broken lines can be obtained as limits of those curves. The corresponding deformation can be viewed as a quantization, in which the broken line is a classical object and the curves are quantum. This generalizes to a new connection between algebraic geometry and the geometry of polyhedra, which is more straight-forward than the other known connections and gives a new insight into constructions used in the topology of real algebraic varieties.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-06-06T21:25:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "00A99"
    ],
    "keywords": [
      "real algebraic geometry",
      "logarithmic paper",
      "real algebraic curves look",
      "dequantization",
      "real algebraic varieties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......5163V"
    }
  }
}