{
  "abstract": "We obtain bounds for the $F$-pure threshold of isolated hypersurface singularities over an algebraically closed field of positive characteristic $p$ in terms of classical singularity invariants. For an irreducible plane curve whose value semigroup has first two generators $β_0,β_1$, we show that the $F$-pure threshold is at most $\\frac{1}{β_0}+\\frac{1}{β_1}$ and differs from it by less than $\\frac{1}{\\gcd(β_0,β_1)p}$, with equality when certain base-$p$ digits add without carrying, and we give an example showing that higher weighted-order terms can change the $F$-pure threshold. We also conjecture a lower bound in terms of the Milnor number, and prove it for semi-quasi-homogeneous singularities, for all plane curves, and whenever the number of variables exceeds $p$. In particular, it holds in characteristic $2$. As applications, we reprove Igusa's formula for the log canonical threshold of a complex plane branch (with integer coefficients), prove the conjecture of Mustaţă, Takagi and Watanabe for such branches, and bound the log canonical threshold of complex isolated hypersurface singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.04014",
  "author_total": 1,
  "authors": [
    {
      "name": "Yotam Svoray"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8mqgk5pdpmfy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.04014",
  "fulltext_url": null,
  "id": "a8mqgk5pdpmfy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.04014",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7163519092",
  "pdf_url": "https://arxiv.org/pdf/2606.04014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8mqgk5pdpmfy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2606.04014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.04014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bounds on the F-Pure Threshold of Isolated Hypersurface Singularities",
  "title_text": "Bounds on the F-Pure Threshold of Isolated Hypersurface Singularities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/a8mqgk5pdpmfy",
  "venue": "arXiv",
  "versions": []
}