{
  "id": "math/0210417",
  "version": "v2",
  "published": "2002-10-27T20:34:41.000Z",
  "updated": "2002-11-11T14:22:51.000Z",
  "title": "Noncommutative ampleness for multiple divisors",
  "authors": [
    "Dennis S. Keeler"
  ],
  "comment": "11 pages, LaTeX, minor corrections, to appear in J. Algebra",
  "journal": "J. Algebra 265 (2003), no. 1, 299--311.",
  "doi": "10.1016/S0021-8693(03)00126-1",
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "The twisted homogeneous coordinate ring is one of the basic constructions of the noncommutative projective geometry of Artin, Van den Bergh, and others. Chan generalized this construction to the multi-homogeneous case, using a concept of right ampleness for a finite collection of invertible sheaves and automorphisms of a projective scheme. From this he derives that certain multi-homogeneous rings, such as tensor products of twisted homogeneous coordinate rings, are right noetherian. We show that right and left ampleness are equivalent and that there is a simple criterion for such ampleness. Thus we find under natural hypotheses that multi-homogeneous coordinate rings are noetherian and have integer GK-dimension.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-11T14:22:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A22",
      "16S38",
      "14F17"
    ],
    "keywords": [
      "multiple divisors",
      "noncommutative ampleness",
      "twisted homogeneous coordinate ring",
      "van den bergh",
      "tensor products"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10417K"
    }
  }
}