{
  "abstract": "Let $X$ be a smooth projective complex surface. We obtain explicit formulas for the Chern character operators on the Hilbert schemes of points $X^{[n]}$ in terms of Nakajima operators, determining in particular the coefficients of the terms involving the canonical class $K_X$ and its square. Consequently, the cohomology ring structure of the Hilbert scheme is determined. As an application, we give an alternative proof of the action of the affine Yangian $Y_{t_1,t_2}(\\widehat{\\mathfrak{gl}}_1)$ on the cohomological Fock space $\\mathbb{H}_X = \\bigoplus_{n\\geq 0} H^*(X^{[n]},\\mathbb{Q})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14491",
  "author_total": 2,
  "authors": [
    {
      "name": "Wei-Ping Li"
    },
    {
      "name": "Zhongyi Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9f532nndraf14.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14491",
  "fulltext_url": null,
  "id": "9f532nndraf14",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14491",
  "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": "W7221823771",
  "pdf_url": "https://arxiv.org/pdf/2610.14491",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9f532nndraf14.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14491",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14491"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The canonical class and Chern character operators on Hilbert schemes of points",
  "title_text": "The canonical class and Chern character operators on Hilbert schemes of points",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9f532nndraf14",
  "venue": "arXiv",
  "versions": []
}