{
  "abstract": "We investigate the notion of holomorphic $p$-contact structure, that we introduced recently in the scalar case with H. Kasuya and L. Ugarte and in the line-bundle case with K. Broder, in the context of a holomorphic family of compact complex manifolds equipped with a holomorphic family of holomorphic line bundles. Firstly, we show that the existence of a holomorphic $p$-contact structure is {\\bf deformation-open} when a non-jumping assumption is made on the $\\bar\\partial$-cohomology of bidegree $(p,\\,0)$. This ought to become a source of further examples of holomorphic $p$-contact manifolds. Secondly, we obtain a Berndtsson-type {\\bf (semi-)positivity} result for the holomorphic vector bundle over the base induced, as a direct image, by the line bundle on the total space that supports the p-contact structures. Thirdly, we introduce a moduli space of relative holomorphic p-contact structures and we show that it is {\\bf Hausdorff} and {\\bf open} in a certain quotient topological space.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20430",
  "author_total": 1,
  "authors": [
    {
      "name": "Dan Popovici"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6910hswx886yh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20430",
  "fulltext_url": null,
  "id": "6910hswx886yh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20430",
  "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": "W7222162028",
  "pdf_url": "https://arxiv.org/pdf/2610.20430",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6910hswx886yh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20430",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20430"
    }
  ],
  "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": "Deformations of Holomorphic $p$-Contact Structures",
  "title_text": "Deformations of Holomorphic p-Contact Structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/6910hswx886yh",
  "venue": "arXiv",
  "versions": []
}