{
  "id": "1103.2926",
  "version": "v6",
  "published": "2011-03-15T14:47:16.000Z",
  "updated": "2017-03-16T16:35:26.000Z",
  "title": "An incidence theorem in higher dimensions",
  "authors": [
    "Jozsef Solymosi",
    "Terence Tao"
  ],
  "comment": "26 pages, no figures. A gap in the proof of Proposition 4.4 has been repaired",
  "journal": "Discrete Comput. Geom. 48 (2012), no. 2, 255-280",
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "We prove almost tight bounds on incidences between points and $k$-dimensional varieties of bounded degree in $\\R^d$. Our main tools are the Polynomial Ham Sandwich Theorem and induction on both the dimension and the number of points.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-02-20T02:56:06.000Z",
      "comment": "26 pages, no figures, submitted, Disc. Comp. Geom. This is the final version",
      "journal": null,
      "doi": null
    },
    {
      "version": "v6",
      "updated": "2017-03-16T16:35:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52C10",
      "32S22"
    ],
    "keywords": [
      "higher dimensions",
      "incidence theorem",
      "polynomial ham sandwich theorem",
      "dimensional varieties",
      "tight bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2926S"
    }
  }
}