{
  "abstract": "Let $X$ be the moduli space of stable trace-free rank $r$ Higgs bundles over a smooth projective curve $C$ with fixed determinant $Λ\\in\\Pic(C)$ and $\\gcd(r,\\degΛ)=1$. We prove that the $\\cc^*$-equivariant quantum product of a divisor on $X$ is given by the Steinberg correspondence of the Lagrangian Steinberg cycle in $X\\times X$. The Steinberg cycle is the image of the reduced virtual fundamental cycle of the $2$-pointed Kontsevich stable map space to $X$ under evaluation map. For $Γ=\\Pic^0(C)[r]$, we give a character decomposition for $Γ$-invariant curve classes or finite orbit sums. In rank two and genus two we explicitly determine its fifteen endoscopic lines and the reduced spectral discriminant. %The resulting endoscopic support statement is cohomological, not a determination of the entire Chow cycle. For $\\widehat X=[X/Γ]$, which is the moduli space of stable $\\PGL_r$-Higgs bundles over $C$. We consider the orbifold quantum cohomology theory from a gerbe-twisted theory. The complex K-theory $\\KU^*(X)$ and twisted K-theory $\\KU^*([X/Γ],α)$ by the lifting $μ_r$-gerbe $α$ of the universal projective bundle is an isomorphism, and is given by the Fourier-Mukai transformation. We prove that the Fourier-Mukai transformation is compatible with the quantum product by the divisors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03520",
  "author_total": 2,
  "authors": [
    {
      "name": "Yunfeng Jiang"
    },
    {
      "name": "Hsian-Hua Tseng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6k75ge2ga0s19.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03520",
  "fulltext_url": null,
  "id": "6k75ge2ga0s19",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03520",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7220439012",
  "pdf_url": "https://arxiv.org/pdf/2610.03520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6k75ge2ga0s19.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.03520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quantum cohomology, Hitchin systems, and Fourier--Mukai comparison",
  "title_text": "Quantum cohomology, Hitchin systems, and Fourier--Mukai comparison",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/6k75ge2ga0s19",
  "venue": "arXiv",
  "versions": []
}