{
  "abstract": "We construct, through Hodge-theoretical methods, what we call the $E_r$-Jacobian torus, the $E_r$-Albanese torus and the $E_r$-Albanese map of any compact complex manifold that is either {\\it page-(r-1)-$\\partial\\bar\\partial$} or {\\it $E_r$-sGG}. These two classes of manifolds, the former of which is contained in the latter, have been introduced recently by both authors jointly with J. Stelzig, respectively by the first-named author. A Hodge theory is also developed for the latter class of manifolds. We then apply our results to give structure theorems and an identity of algebraic dimensions in terms of the $E_r$-Albanese map and torus. Other applications result in cohomological and metrical theorems for the $6$-dimensional sphere when it is equipped either with a hypothetical complex structure or with the complex structures very recently claimed to exist in the literature. For example, we show that in the latter case no {\\it strongly Gauduchon} metric exists on $S^6$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02109",
  "author_total": 2,
  "authors": [
    {
      "name": "Dan Popovici"
    },
    {
      "name": "Luis Ugarte"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/661n51rwzfn7z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02109",
  "fulltext_url": null,
  "id": "661n51rwzfn7z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02109",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7216479419",
  "pdf_url": "https://arxiv.org/pdf/2610.02109",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/661n51rwzfn7z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02109",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02109"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher-Page Jacobian and Albanese Tori",
  "title_text": "Higher-Page Jacobian and Albanese Tori",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/661n51rwzfn7z",
  "venue": "arXiv",
  "versions": []
}