{
  "abstract": "The limiting Hodge structure relates the geometric degeneration of varieties to its Hodge-theoretic behavior. We study degenerations of cubic hypersurfaces whose singular central fibers are secant cubics. The pertinent degenerations of cubic threefolds and fourfolds have been extensively studied for compactifying the associated moduli spaces. In the two cases, the secant cubics are constructed by the rational normal quartic and the Veronese surface, respectively. The Veronese surface is a Severi variety, and the rational normal quartic is a hyperplane section of it. In eariler work, we investigated degenerations to the secant cubics of higher-dimensional Severi varieties. Here we study the limiting Hodge structures for degenerations to their hyperplane sections.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11198",
  "author_total": 2,
  "authors": [
    {
      "name": "Renjie Lyu"
    },
    {
      "name": "Xuanyu Pan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4489tfnpf623p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11198",
  "fulltext_url": null,
  "id": "4489tfnpf623p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11198",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7168265048",
  "pdf_url": "https://arxiv.org/pdf/2607.11198",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4489tfnpf623p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.11198",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11198"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Limiting Hodge Structures for Cubic Hypersurfaces of Secant Type",
  "title_text": "Limiting Hodge Structures for Cubic Hypersurfaces of Secant Type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4489tfnpf623p",
  "venue": "arXiv",
  "versions": []
}