{
  "id": "2209.11369",
  "version": "v1",
  "published": "2022-09-23T01:59:50.000Z",
  "updated": "2022-09-23T01:59:50.000Z",
  "title": "Infinitesimal structure of log canonical thresholds",
  "authors": [
    "Jihao Liu",
    "Fanjun Meng",
    "Lingyao Xie"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We show that log canonical thresholds of fixed dimension are standardized. More precisely, we show that any sequence of log canonical thresholds in fixed dimension $d$ accumulates in a way which is i) either similar to how standard and hyperstandard sets accumulate, or ii) to log canonical thresholds in dimension $\\leq d-2$. This provides an accurate description on the infinitesimal structure of the set of log canonical thresholds. We also discuss similar behaviors of minimal log discrepancies, canonical thresholds, and K-semistable thresholds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-23T01:59:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14E30",
      "14B05"
    ],
    "keywords": [
      "log canonical thresholds",
      "infinitesimal structure",
      "minimal log discrepancies",
      "fixed dimension",
      "hyperstandard sets accumulate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}