{
  "id": "2007.11995",
  "version": "v1",
  "published": "2020-07-21T14:59:25.000Z",
  "updated": "2020-07-21T14:59:25.000Z",
  "title": "Algebraic intersection for translation surfaces in the stratum $\\mathcal{H}(2)$",
  "authors": [
    "Smaïl Cheboui",
    "Arezki Kessi",
    "Daniel Massart"
  ],
  "comment": "8 pages, 3 figures. arXiv admin note: text overlap with arXiv:2007.10847",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the quantity $\\mbox{KVol}$ defined as the supremum, over all pairs of closed curves, of their algebraic intersection, divided by the product of their lengths, times the area of the surface. The surfaces we consider live in the stratum $\\mathcal{H}(2)$ of translation surfaces of genus $2$, with one conical point. We provide an explicit sequence $L(n,n)$ of surfaces such that $\\mbox{KVol}(L(n,n)) \\longrightarrow 2$ when $n$ goes to infinity, $2$ being the conjectured infimum for $\\mbox{KVol}$ over $\\mathcal{H}(2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-21T14:59:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D40",
      "37D50"
    ],
    "keywords": [
      "translation surfaces",
      "algebraic intersection",
      "explicit sequence",
      "closed curves",
      "conical point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}