{
  "abstract": "The Chern-Schwartz-MacPherson class $c_{SM}(X)$ is defined in the Chow group $A_*(X)$ of a scheme $X$, and generalizes $c(T_X)\\cap [X]$ if $X$ is smooth. In this paper we independently compute $c_{SM}(S^nX)\\in A_*(S^nX)$ modulo $n!$ torsion; we use this result to compute the pushforward to $S^nX$ of $c_{SM}(Quot^n_X(E))$ (and in particular $c_{SM}(Hilb^n X)$) when $X$ is smooth and $E$ is a vector bundle on $X$. Finally, when $X$ is smooth and complete of dimension $3$ we propose a refined version of the the MNOP conjecture that computes the image of the pushforward of $[Hilb^n X]^{vir}$ to $A_0(S^nX)$ and prove it modulo $n!$ torsion when $X$ is Calabi-Yau.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31826",
  "author_total": 2,
  "authors": [
    {
      "name": "Barbara Fantechi"
    },
    {
      "name": "Lothar Goettsche"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91f89v221j68y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31826",
  "fulltext_url": null,
  "id": "91f89v221j68y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31826",
  "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": "W7223682473",
  "pdf_url": "https://arxiv.org/pdf/2610.31826",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91f89v221j68y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.31826",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31826"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Chern-Schwartz-MacPherson classes of symmetric powers and applications",
  "title_text": "Chern-Schwartz-MacPherson classes of symmetric powers and applications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/91f89v221j68y",
  "venue": "arXiv",
  "versions": []
}