{
  "abstract": "We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra $H_*(\\N^{\\pl},\\Q)$ of the projective-linear pairs stack, and next pass to Gross's polynomial realization $e^κ\\Q[s_{jk\\ell}]$. We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on $\\PP^3$, on a smooth cubic threefold, on $\\Bl_p\\PP^3$, on $\\Bl_\\ell\\PP^3$, and on the projective-bundle threefold $\\PP(\\OO_X\\oplus \\OO_X(-1,-1))$ over $X=\\PP^1\\times\\PP^1$. In the $\\PP^3$ and cubic threefold examples we compare the intrinsic large-$n$ tails with the formulas of Pandharipande and Moreira and show that, in the cases treated in common, the differences are Laurent polynomials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.02526",
  "author_total": 1,
  "authors": [
    {
      "name": "Reginald Anderson"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/417qr718vtas1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02526",
  "fulltext_url": null,
  "id": "417qr718vtas1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02526",
  "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.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7167602388",
  "pdf_url": "https://arxiv.org/pdf/2607.02526",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/417qr718vtas1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2607.02526",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02526"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing",
  "title_text": "Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/417qr718vtas1",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.13140/rg.2.2.35985.70243",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}