{
  "id": "math/9912051",
  "version": "v2",
  "published": "1999-12-06T22:22:19.000Z",
  "updated": "2000-02-29T03:10:07.000Z",
  "title": "Criteria for σ-ampleness",
  "authors": [
    "Dennis S. Keeler"
  ],
  "comment": "16 pages, LaTeX2e, to appear in J. of the AMS, minor errors corrected (esp. in 1.4 and 3.1), proofs simplified",
  "journal": "J. Amer. Math. Soc. 13 (2000), no. 3, 517-532.",
  "doi": "10.1090/S0894-0347-00-00334-9",
  "categories": [
    "math.AG",
    "math.RA"
  ],
  "abstract": "In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a $\\sigma$-ample divisor, where $\\sigma$ is an automorphism of a projective scheme X. Many open questions regarding $\\sigma$-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be $\\sigma$-ample. As a consequence, we show right and left $\\sigma$-ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms $\\sigma$ yield a $\\sigma$-ample divisor.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-02-29T03:10:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A22",
      "14F17",
      "14J50",
      "16P90",
      "16S38",
      "16W50"
    ],
    "keywords": [
      "ample divisor",
      "noncommutative homogeneous coordinate ring",
      "van den bergh",
      "relatively simple necessary",
      "basic constructions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "J. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12051K"
    }
  }
}