{
  "id": "1102.0787",
  "version": "v2",
  "published": "2011-02-03T21:13:43.000Z",
  "updated": "2011-04-04T13:48:44.000Z",
  "title": "On the canonical map of surfaces with q>=6",
  "authors": [
    "Margarida Mendes Lopes",
    "Rita Pardini",
    "Gian Pietro Pirola"
  ],
  "comment": "Dedicated to Fabrizio Catanese on the occasion of his 60th birthday. To appear in the special issue of Science of China Ser.A: Mathematics dedicated to him. V2:some typos have been corrected",
  "categories": [
    "math.AG"
  ],
  "abstract": "We carry out an analysis of the canonical system of a minimal complex surface of general type with irregularity q>0. Using this analysis we are able to sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7. Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a curve of genus >1. We prove that for q>=6 the canonical map is birational. Combining this result with the analysis of the canonical system, we also prove the inequality: K^2>=7\\chi+2. This improves an earlier result of the first and second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in Geom. 10 (3) (2010), 549-555].",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-04-04T13:48:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29"
    ],
    "keywords": [
      "canonical map",
      "canonical system",
      "minimal complex surface",
      "second author",
      "castelnuovo inequality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11425-011-4200-2",
      "journal": "Science in China A: Mathematics",
      "year": 2011,
      "month": "Aug",
      "volume": 54,
      "number": 8,
      "pages": 1725
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011ScChA..54.1725M"
    }
  }
}