{
  "id": "2201.07710",
  "version": "v1",
  "published": "2022-01-19T16:51:15.000Z",
  "updated": "2022-01-19T16:51:15.000Z",
  "title": "A Riemann-Roch theorem on a weighted infinite graph",
  "authors": [
    "Atsushi Atsuji",
    "Hiroshi Kaneko"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "A Riemann-Roch theorem on graph was initiated by M. Baker and S. Norine. In their article [2], a Riemann-Roch theorem on a finite graph with uniform vertex-weight and uniform edge-weight was established and it was suggested a Riemann-Roch theorem on an infinite graph was feasible. In this article, we take an edge-weighted infinite graph and focus on the importance of the spectral gaps of the Laplace operators defined on its finite subgraphs naturally given by Q-valued positive weights on the edges. We build a potential theoretic scheme for proof of a Riemann-Roch theorem on the edge-weighted infinite graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-19T16:51:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann-roch theorem",
      "edge-weighted infinite graph",
      "potential theoretic scheme",
      "uniform edge-weight",
      "spectral gaps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}