{
  "id": "2312.15397",
  "version": "v1",
  "published": "2023-12-24T03:47:46.000Z",
  "updated": "2023-12-24T03:47:46.000Z",
  "title": "On the equivalence between the effective adjunction conjectures of Prokhorov-Shokurov and of Li",
  "authors": [
    "Jingjun Han",
    "Jihao Liu",
    "Qingyuan Xue"
  ],
  "comment": "13 pages. arXiv admin note: text overlap with arXiv:2309.15823",
  "categories": [
    "math.AG",
    "math.DS"
  ],
  "abstract": "Prokhorov and Shokurov introduced the famous effective adjunction conjecture, also known as the effective base-point-freeness conjecture. This conjecture asserts that the moduli component of an lc-trivial fibration is effectively base-point-free. Li proposed a variation of this conjecture, which is known as the $\\Gamma$-effective adjunction conjecture, and proved that a weaker version of his conjecture is implied by the original Prokhorov-Shokurov conjecture. In this paper, we establish the equivalence of Prokhorov-Shokurov's and Li's effective adjunction conjectures. The key to our proof is the formulation of a uniform rational polytope for canonical bundle formulas, which relies on recent developments in the minimal model program theory of algebraically integrable foliations by Ambro-Cascini-Shokurov-Spicer and Chen-Han-Liu-Xie.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-24T03:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "37F75"
    ],
    "keywords": [
      "equivalence",
      "minimal model program theory",
      "uniform rational polytope",
      "lis effective adjunction conjectures",
      "original prokhorov-shokurov conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}