{
  "abstract": "Let $X$ be a cominuscule Grassmannian (equivalently, an irreducible Hermitian symmetric space), and let $p$ be an integer. We compute the minimum $l(p)$ such that $H^0(\\Omega_X^p(l(p))) \\neq 0$. This allows us to conclude that any codimension-one foliation of degree zero on a cominuscule Grassmannian is a pencil of hyperplanes, improving a result of the first and third authors with D. Faenzi. We also deduce the structure of codimension-one foliations of degree one. Finally, we provide families of examples of high codimensional foliations of minimal degree on classical Grassmannians, Lagrangian Grassmannians, Spinor varieties, and the Cayley plane.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2604.05553",
  "author_total": 3,
  "authors": [
    {
      "name": "Vladimiro Benedetti"
    },
    {
      "name": "Crislaine Kuster"
    },
    {
      "name": "Alan Muniz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9cx54wcnje2x3.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "9cx54wcnje2x3",
  "issns": [],
  "landing_url": "https://hal.science/hal-05580248v3",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ag"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05580248/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9cx54wcnje2x3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05580248",
      "source": "hal",
      "url": "https://hal.science/hal-05580248v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ag",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Minimal-Degree Foliations on Cominuscule Grassmannians",
  "title_text": "Minimal-Degree Foliations on Cominuscule Grassmannians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/9cx54wcnje2x3",
  "venue": "HAL",
  "versions": []
}