{
  "abstract": "For a compact oriented even-dimensional Witt pseudomanifold $X$, we compute the $S_n$-equivariant Banagl--Zagier $L$-classes of $X^n$ in terms of the Goresky--MacPherson $L$-classes of $X$ and the intersection cohomology Euler characteristic of $X$. This generalizes a theorem of Zagier for manifolds. Our approach is based on analyzing the equivariant structure of the signature operator of $X^n$ using equivariant $KK$-theory and power operations in analytic $K$-homology. We establish an analytic $K$-homology analogue of Moonen's algebraic localization theorem by proving that the localized Chern character of the $n$-th power operation, evaluated at an $n$-cycle, agrees with the $n$-th homological Adams operation applied to the Chern character. As an application, we prove that the characteristic class Hodge index conjecture for singular varieties, formulated by Brasselet--Schürmann--Yokura, is preserved under taking symmetric products of complex projective varieties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02577",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammadali Aligholi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fhrfdx1rcna73.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02577",
  "fulltext_url": null,
  "id": "fhrfdx1rcna73",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02577",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02577",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fhrfdx1rcna73.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02577",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02577"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "$S_n$-equivariant $L$-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products",
  "title_text": "S_n-equivariant L-classes of Cartesian powers of Witt spaces and the Hodge index conjecture for symmetric products",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/fhrfdx1rcna73",
  "venue": "arXiv",
  "versions": []
}