{
  "id": "2212.02556",
  "version": "v1",
  "published": "2022-12-05T19:21:53.000Z",
  "updated": "2022-12-05T19:21:53.000Z",
  "title": "Webs by conics on del Pezzo surfaces and hyperlogarithmic functional identities",
  "authors": [
    "Luc Pirio"
  ],
  "comment": "Long preliminary version, not intended to be published in this form in a peer reviewed journal. 49 pages, 2 figures",
  "categories": [
    "math.AG",
    "math.CV",
    "math.DG"
  ],
  "abstract": "For $d$ ranging from 2 to 6, we prove that the web by conics naturally defined on any smooth del Pezzo surface of degree $d$ carries an interesting functional identity whose components all are a certain antisymmetric hyperlogarithm of weight $7-d$. Our approach is uniform with respect to $d$ and at the end relies on classical results about the action of Weyl groups on the set of lines contained in the considered del Pezzo surface. This series of `del Pezzo's hyperlogarithmic functional identities' is a natural generalization of the famous and well-know 3-term and 5-term identities of the logarithm and dilogarithm ('Abel's relation') which correspond to the cases when $d=6$ and $d=5$ respectively. This text ends with a section containing several questions and some possibly interesting perspectives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-05T19:21:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "33E20",
      "39B32",
      "14J26",
      "14C21",
      "53A60"
    ],
    "keywords": [
      "functional identity",
      "del pezzos hyperlogarithmic functional identities",
      "smooth del pezzo surface",
      "antisymmetric hyperlogarithm",
      "end relies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 49,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}