{
  "id": "math/0611396",
  "version": "v1",
  "published": "2006-11-13T17:36:12.000Z",
  "updated": "2006-11-13T17:36:12.000Z",
  "title": "Complex orientations of real algebraic surfaces",
  "authors": [
    "Oleg Viro"
  ],
  "journal": "Advances in Soviet Math., vol. 18, 1994, 261-284",
  "categories": [
    "math.AG",
    "math.GT"
  ],
  "abstract": "We study natural additional structures on real algebraic surfaces with trivial first homology mod 2 of the complexification. If the set of real points realizes the zero of the second homology mod 2 of the complexification, then the set of real points is equipped with a pair of opposite orientations and a Spin structure. If the set of real points realizes the same homology class as the complexification of a real curve on the surface, then the complement of the curve in set of real points is equipped a pair of opposite orientations, which do not extend across the curve, and the whole set of real points is equipped with a Pin^- structure. These constructions are similar to the complex orientations of real algebraic curves dividing their complexifications and generalize to high dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-13T17:36:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14P25",
      "14F25",
      "14F45"
    ],
    "keywords": [
      "real algebraic surfaces",
      "complex orientations",
      "real points realizes",
      "trivial first homology mod",
      "complexification"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11396V"
    }
  }
}