{
  "abstract": "Let $X$ be a smooth projective complex surface with numerically trivial canonical class. With the help of GPT-5.6 Sol, we prove Qin's conjecture that the reduced generating series of intersection numbers of Chern characters of tautological bundles against the total Chern class of $X^{[n]}$ is a quasimodular form with the predicted mixed-weight bound. The main ingredient is a Wick's theorem-type formula for computing traces of normally ordered products of Nakajima operators on $\\bigoplus_n H^*(X^{[n]})$. Following the argument of Li-Qin-Wang, the computation of the reduced generating series is reduced to computing the constant term of the supertrace of a product of certain operator-valued currents and the Carlsson-Okounkov operator. Our trace formula shows that this supertrace can be expressed in terms of two quasi-elliptic functions $\\widehat Z$, $P$ and a quasimodular function $T$, whose constant terms are quasimodular forms by the theorem of Goujard-Moller. Finally, we give an explicit algorithm for computing the general reduced generating series.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33884",
  "author_total": 4,
  "authors": [
    {
      "name": "Victor Alekseev"
    },
    {
      "name": "Avik Chakravarty"
    },
    {
      "name": "Daebeom Choi"
    },
    {
      "name": "Shengjing Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/123zp0j726zt4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33884",
  "fulltext_url": null,
  "id": "123zp0j726zt4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33884",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7214712373",
  "pdf_url": "https://arxiv.org/pdf/2609.33884",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/123zp0j726zt4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.33884",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33884"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Qin's quasimodularity conjecture for Hilbert schemes of points",
  "title_text": "Qin's quasimodularity conjecture for Hilbert schemes of points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/123zp0j726zt4",
  "venue": "arXiv",
  "versions": []
}