{
  "abstract": "Browning and Sawin conjectured that random hypersurfaces with sign coefficients are smooth with probability tending to one as the degree grows. We prove this conjecture and obtain a quantitative bound. For each $n\\geq1$, a degree $d$ form in $n+1$ variables, with independent uniform coefficients in $\\{-1,1\\}$, defines a singular complex hypersurface with probability $O_n(d^{-1/2})$. The positive-dimensional singular loci occur with exponentially small probability. For $n\\geq3$, the same exponential bound holds for failure of absolute irreducibility. These results have been formalized in Lean by AxiomProver assuming existing literature.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18879",
  "author_total": 2,
  "authors": [
    {
      "name": "Ken Ono"
    },
    {
      "name": "Ashvin Swaminathan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/feav0k8334087.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18879",
  "fulltext_url": null,
  "id": "feav0k8334087",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18879",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213523357",
  "pdf_url": "https://arxiv.org/pdf/2609.18879",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/feav0k8334087.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18879",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18879"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients",
  "title_text": "On a conjecture of Browning and Sawin on random hypersurfaces with sign coefficients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/feav0k8334087",
  "venue": "arXiv",
  "versions": []
}