{
  "abstract": "Let $C_{p, 2}(\\mathbb{P}^{n})$ denote the Chow variety parametrizing effective algebraic $p$-cycles of degree two on $\\mathbb{P}^{n}$. We show that its rational cohomology is pure Tate and concentrated in even degrees. An anti-invariant Chern class identity yields a presentation of the cohomology ring as a fiber product, which in turn determines the cohomology over $\\mathbb{Z}[1/2]$. We identify the ordinary Poincaré polynomial with the known virtual formula, determine the optimal ranges over which the coefficients stabilize, and compute the nonrational Poincaré series of the stable space $D(2)$. For the Lawson--Michelsohn map $D(2)\\longrightarrow D(\\infty)$, the first nonzero rational homotopy kernel occurs in degree eight and is one-dimensional, while the integral kernel has rank one. Finally, we compute the relative homology of the pair $(D(2),BU)$ over $\\mathbb{Z}[1/2]$ and show that additional cohomology generators and nonzero rational homotopy kernels arise in unbounded degrees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39498",
  "author_total": 3,
  "authors": [
    {
      "name": "Youming Chen"
    },
    {
      "name": "Wenchuan Hu"
    },
    {
      "name": "Deyuan Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbttk2r9sj6sd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39498",
  "fulltext_url": null,
  "id": "dbttk2r9sj6sd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39498",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39498",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbttk2r9sj6sd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39498",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39498"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Poincaré series of degree-two Chow varieties",
  "title_text": "Poincaré series of degree-two Chow varieties",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/dbttk2r9sj6sd",
  "venue": "arXiv",
  "versions": []
}