{
  "abstract": "We study holomorphic foliations on projective spaces that leave smooth projective complete intersection surfaces $M$ invariant. We determine precisely for which degrees such foliations on $M$ exist. As a consequence, we obtain new bounds for the classical Poincaré problem for smooth projective complete intersection surfaces and prove that previously known bounds for smooth hypersurfaces in $\\mathbb{P}^3$ are optimal. Furthermore, for a foliation $[s]$ on $M$ with isolated singularities and for degrees beyond an explicit bound that we provide, we show that a section $s'$ has singular scheme containing that of $s$ if and only if $s'=ϕ(s)$ for some global endomorphism $ϕ$ of the tangent bundle of $M$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09877",
  "author_total": 2,
  "authors": [
    {
      "name": "Jorge Olivares"
    },
    {
      "name": "Daniel Posada-Buriticá"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6bcgb0pqjff08.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09877",
  "fulltext_url": null,
  "id": "6bcgb0pqjff08",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09877",
  "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": "W7202164512",
  "pdf_url": "https://arxiv.org/pdf/2608.09877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6bcgb0pqjff08.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.09877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces",
  "title_text": "Effective Results for Foliations on Smooth Projective Complete Intersection Surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/6bcgb0pqjff08",
  "venue": "arXiv",
  "versions": []
}