{
  "abstract": "We prove that the Higgs--Demailly system on a compact Riemann surface admits, for suitable fixed parameters, a smooth admissible solution at its terminal parameter if and only if the Higgs bundle is H-ample. Here H-ampleness is understood in the modified sense of Biswas--Misra--Ray. In particular, the argument gives an analytic proof of the equivalence between this H-ampleness and Griffiths-positive Hitchin--Simpson curvature. The proof extends the Demailly--Pingali--Murakami approach using a priori estimates and Leray--Schauder degree theory. The missing scalar lower bound follows from a Higgs-compatible quotient construction: a blow-up sequence produces a nonzero Higgs quotient of nonpositive degree, contradicting H-ampleness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00556",
  "author_total": 1,
  "authors": [
    {
      "name": "Liangdi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/43sv7bkv7qsx8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00556",
  "fulltext_url": null,
  "id": "43sv7bkv7qsx8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00556",
  "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.DG"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7206148984",
  "pdf_url": "https://arxiv.org/pdf/2609.00556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/43sv7bkv7qsx8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.00556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higgs-Demailly System and Positivity of Higgs Bundles",
  "title_text": "Higgs-Demailly System and Positivity of Higgs Bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/43sv7bkv7qsx8",
  "venue": "arXiv",
  "versions": []
}