{
  "id": "2203.02843",
  "version": "v1",
  "published": "2022-03-06T00:54:01.000Z",
  "updated": "2022-03-06T00:54:01.000Z",
  "title": "Effective divisors and Newton-Okounkov bodies of Hilbert schemes of points on toric surfaces",
  "authors": [
    "Ian Cavey"
  ],
  "comment": "41 pages, 3 figures",
  "categories": [
    "math.AG",
    "math.CO"
  ],
  "abstract": "We compute the (unbounded) Newton-Okounkov body of the Hilbert scheme of points on $\\mathbb C^2$. We obtain an upper bound for the Newton-Okounkov body of the Hilbert scheme of points on any smooth toric surface. We conjecture that this upper bound coincides with the exact Newton-Okounkov body for the Hilbert schemes of points on $\\mathbb P^2$, $\\mathbb P^1\\times\\mathbb P^1$, and Hirzebruch surfaces. These results imply upper bounds for the effective cones of these Hilbert schemes, which are also conjecturally sharp in the above cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-06T00:54:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M25"
    ],
    "keywords": [
      "hilbert scheme",
      "effective divisors",
      "smooth toric surface",
      "upper bound coincides",
      "exact newton-okounkov body"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}