{
  "abstract": "Schimpf's connected reformulation of Pandharipande's pole conjecture for stable pairs predicts the following restriction: in class \\(β\\), connected descendent coefficients have nonzero \\(p\\)-poles only where \\(-p\\) is an \\(m\\)-th root of unity with \\(1\\leq m\\leq\\divis(β)\\). We give a toric counterexample. The threefold is a smooth quasi-projective toric Calabi--Yau threefold whose compact torus-invariant curves form a chain \\(C_1\\cup C_2\\). For the primitive class \\(β=2[C_1]+[C_2]\\), the coefficient of \\(Q^βz^3\\) in the connected series for the insertion \\(\\ch_z([v]_T)\\), where \\([v]_T\\) is the equivariant class of \\(v=C_1\\cap C_2\\), has Laurent expansion \\[ {\\frac{9}{4}}\\frac{1}{p-1}+O(1) \\] after restricting to the one-parameter subtorus with tangent weights \\((1,2,-3)\\) at \\(v\\). Since \\(\\divis(β)=1\\), Schimpf's condition allows only the nonzero pole \\(p=-1\\). The pole at \\(p=1\\) is therefore forbidden.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06876",
  "author_total": 1,
  "authors": [
    {
      "name": "Reginald Anderson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/64wd9wjvfnzcx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06876",
  "fulltext_url": null,
  "id": "64wd9wjvfnzcx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06876",
  "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.AG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.06876",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/64wd9wjvfnzcx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.06876",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06876"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A toric Calabi-Yau counterexample to Schimpf's connected stable pairs pole conjecture",
  "title_text": "A toric Calabi-Yau counterexample to Schimpf's connected stable pairs pole conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/64wd9wjvfnzcx",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.13140/rg.2.2.18652.96649",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}