{
  "abstract": "Let $V$ be a complex symplectic vector space and let $\\mathbb{P}(V)$ carry the induced contact structure and symplectic polarity. We study the loci of hypersurfaces containing codimension-two cones supported on hyperplanes. The starting point is the following characterization: a projective subvariety $X\\subset\\mathbb{P}(V)$ which is a hypersurface of degree at least two in a hyperplane $H$ is involutive if and only if it is a cone whose vertex contains the polar point $σ(H)$. We give a short proof, construct the corresponding incidence spaces, compute their dimensions and express the incidence degrees as Segre-class integrals. In $\\mathbb{P}^3$ the incidence map is birational for every $d\\ge m\\ge 2$ except $(m,d)=(2,2)$, and the same holds in $\\mathbb{P}^5$; the quadratic case is exceptional in every dimension, the incidence having generic degree $2n$ in $\\mathbb{P}^{2n-1}$. We also give a sufficient criterion for birationality in higher dimension, closed formulas in $\\mathbb{P}^3$ and coefficient formulas in $\\mathbb{P}^5$. For quadric cones in $\\mathbb{P}^5$ the degree is the product of shifted binomial factors and an irreducible polynomial of degree 36, and we explain where the shifted factors come from.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19427",
  "author_total": 1,
  "authors": [
    {
      "name": "Gabriel A. Guedes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2m4p08qddrq20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19427",
  "fulltext_url": null,
  "id": "2m4p08qddrq20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19427",
  "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.SG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7213610913",
  "pdf_url": "https://arxiv.org/pdf/2609.19427",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2m4p08qddrq20.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19427",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19427"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Hypersurfaces containing involutive cones in projective symplectic spaces",
  "title_text": "Hypersurfaces containing involutive cones in projective symplectic spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/2m4p08qddrq20",
  "venue": "arXiv",
  "versions": []
}