{
  "id": "1511.02261",
  "version": "v1",
  "published": "2015-11-06T23:27:09.000Z",
  "updated": "2015-11-06T23:27:09.000Z",
  "title": "Real algebraic surfaces with many handles in $(\\mathbb{CP}^1)^3$",
  "authors": [
    "Arthur Renaudineau"
  ],
  "comment": "29 pages, 8 figures",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this text, we study Viro's conjecture and related problems for real algebraic surfaces in $(\\mathbb{CP}^1)^3$. We construct a counter-example to Viro's conjecture in tridegree $(4,4,2)$ and a family of real algebraic surfaces of tridegree $(2k,2l,2)$ in $(\\mathbb{CP}^1)^3$ with asymptotically maximal first Betti number of the real part. To perform such constructions, we consider double covers of blow-ups of $(\\mathbb{CP}^1)^2$ and we glue singular curves with special position of the singularities adapting the proof of Shustin's theorem for gluing singular hypersurfaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-06T23:27:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real algebraic surfaces",
      "asymptotically maximal first betti number",
      "glue singular curves",
      "study viros conjecture",
      "real part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102261R"
    }
  }
}