{
  "abstract": "Let $(M,ω)$ be a closed connected symplectic manifold of dimension $2n$,. We discuss weighted Fujiki--Donaldson theory with respect to the measure $dν=e^hω^n/n! $ for an arbitrary smooth real-valued function $h$ on $M$. We prove that the group generated by the flows of Hamiltonians that Poisson-commute with $h$ always admits an equivariant moment map for its action on the full space of $ω$-compatible almost complex structures. The moment map takes values in the continuous dual of the Lie algebra. Its density is expressed in terms of the Hermitian scalar curvature, a local weight correction, and an $L^\\infty$ function $r_h^0$ constructed from the long-time average of the polar determinant phase. The function $r_h^0$ can be regarded as a Ruelle-type asymptotic density incorporating phase comparison via a connection. The key step in the proof is to represent the Ricci cocycle as the coboundary of a continuous cochain constructed from $r_h^0$. We also consider the action of the exact volume-preserving diffeomorphism group on a connected component of the space of almost complex structures inducing the given orientation on a closed connected oriented manifold of real dimension $2n$. In contrast to the weighted Hamiltonian setting, we prove that, for $n>1$, this action admits an equivariant moment map if and only if the real first Chern class vanishes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24543",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryushi Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7tdzbp7zt4997.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24543",
  "fulltext_url": null,
  "id": "7tdzbp7zt4997",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24543",
  "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.DG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223028251",
  "pdf_url": "https://arxiv.org/pdf/2610.24543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7tdzbp7zt4997.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Equivariant Moment Maps and the Ricci Cocycle in Weighted Fujiki--Donaldson Theory",
  "title_text": "Equivariant Moment Maps and the Ricci Cocycle in Weighted Fujiki--Donaldson Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/7tdzbp7zt4997",
  "venue": "arXiv",
  "versions": []
}