{
  "id": "math/0010323",
  "version": "v2",
  "published": "2000-10-31T19:22:35.000Z",
  "updated": "2001-01-17T23:21:28.000Z",
  "title": "Zariski theorems and diagrams for braid groups",
  "authors": [
    "David Bessis"
  ],
  "comment": "21 pages",
  "doi": "10.1007/s002220100155",
  "categories": [
    "math.GR",
    "math.AT"
  ],
  "abstract": "Empirical properties of generating systems for complex reflection groups and their braid groups have been observed by Orlik-Solomon and Brou\\'e-Malle-Rouquier, using Shephard-Todd classification. We give a general existence result for presentations of braid groups, which partially explains and generalizes the known empirical properties. Our approach is invariant-theoretic and does not use the classification. The two ingredients are Springer theory of regular elements and a Zariski-like theorem.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-01-17T23:21:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36"
    ],
    "keywords": [
      "braid groups",
      "zariski theorems",
      "complex reflection groups",
      "general existence result",
      "empirical properties"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2001,
      "month": "Sep",
      "volume": 145,
      "number": 3,
      "pages": 487
    },
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001InMat.145..487B"
    }
  }
}