{
  "id": "2405.21062",
  "version": "v1",
  "published": "2024-05-31T17:51:00.000Z",
  "updated": "2024-05-31T17:51:00.000Z",
  "title": "Algebra of global sections of $ψ$-bundles on $\\bar{M}_{0,n}$",
  "authors": [
    "Alexander Polishchuk",
    "Eric Rains"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We consider the ${\\mathbb Z}^n$-graded algebra of global sections of line bundles generated by the standard line bundles $L_1,\\ldots,L_n$ on $\\bar{M}_{0,n}$. We find a simple presentation of this algebra by generators and quadratic relations. As an application we prove that the moduli space $\\bar{M}_{0,n}[\\psi]$ of $\\psi$-stable curves of genus $0$ is Cohen-Macaulay and normal, and the natural map $\\bar{M}_{0,n}\\to \\bar{M}_{0,n}[\\psi]$ is a rational resolution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-31T17:51:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global sections",
      "standard line bundles",
      "quadratic relations",
      "natural map",
      "rational resolution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}