{
  "id": "2206.13977",
  "version": "v1",
  "published": "2022-06-28T13:02:42.000Z",
  "updated": "2022-06-28T13:02:42.000Z",
  "title": "Some characterizations of the complex projective space via Ehrhart polynomials",
  "authors": [
    "Andrea Loi",
    "Fabio Zuddas"
  ],
  "comment": "10 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "Let $P_{\\lambda\\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\\lambda$ of the standard symplex $\\Sigma_n \\subset \\mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold with associated Delzant polytope $\\Delta$ and Ehrhart polynomial $P_\\Delta$ such that $P_{\\Delta}=P_{\\lambda\\Sigma_n}$, for some $\\lambda \\in \\mathbb{Z}^+$, then $(M, L)\\cong (\\mathbb{C} P^n, O(\\lambda))$ (where $O(1)$ is the hyperplane bundle on $\\mathbb{C} P^n$) in the following three cases: 1. arbitrary $n$ and $\\lambda=1$, 2. $n=2$ and $\\lambda =3$, 3. $\\lambda =n+1$ under the assumption that the polarization $L$ is asymptotically Chow semistable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-28T13:02:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C55",
      "32Q15",
      "32T15"
    ],
    "keywords": [
      "ehrhart polynomial",
      "complex projective space",
      "characterizations",
      "dimensional polarized toric manifold",
      "standard symplex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}