{
  "id": "math/0111052",
  "version": "v1",
  "published": "2001-11-06T16:57:25.000Z",
  "updated": "2001-11-06T16:57:25.000Z",
  "title": "On the Canonical Ring of Covers of Surfaces of Minimal Degree",
  "authors": [
    "Francisco J. Gallego",
    "B. P. Purnaprajna"
  ],
  "comment": "22 pages, amstex",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let f be a generically finite morphism from X to Y. The purpose of this paper is to show how the O_Y algebra structure on the push forward of O_X controls algebro-geometric aspects of X like the ring generation of graded rings associated to X and the very ampleness of line bundles on X. As the main application of this we prove some new results for certain regular surfaces X of general type. Precisely, we find the degrees of the generators of the canonical ring of X when the canonical morphism of X is a finite cover of a surface of minimal degree. These results complement results of Ciliberto [Ci] and Green [G]. The techniques of this paper also yield different proofs of some earlier results, such as Noether's theorem for certain kinds of curves and some results on Calabi-Yau threefolds that had appeared in [GP2].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-06T16:57:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J32"
    ],
    "keywords": [
      "minimal degree",
      "canonical ring",
      "controls algebro-geometric aspects",
      "results complement results",
      "calabi-yau threefolds"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11052G"
    }
  }
}