{
  "abstract": "Let $F=(f_1,\\dots,f_r)$ be a family of nonzero polynomials on $\\mathbb C^n$. More than ten years ago, Budur conjectured that $B_F$, the Bernstein--Sato ideal of $F$, is generated by products of linear polynomials with rational coefficients. With the aid of AI, we construct two counterexamples to Budur's conjecture. The examples indicate that main results in [Wu26] provide the optimal linearity properties that the zero locus of Bernstein-Sato ideals satisfies in general.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32287",
  "author_total": 1,
  "authors": [
    {
      "name": "Lei Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bg6hy7adee6x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32287",
  "fulltext_url": null,
  "id": "5bg6hy7adee6x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32287",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7214707380",
  "pdf_url": "https://arxiv.org/pdf/2609.32287",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bg6hy7adee6x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32287",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32287"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Bernstein--Sato ideals might not be linear",
  "title_text": "Bernstein--Sato ideals might not be linear",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5bg6hy7adee6x",
  "venue": "arXiv",
  "versions": []
}