{
  "abstract": "We study singularities of rational inner functions (RIFs) $ϕ$ in three and more variables. We focus on curve and higher-dimensional singularities of $ϕ$ in $\\mathbb{T}^n$ and we show that, under certain conditions, derivative integrability conditions of partial derivatives of $ϕ=\\frac{q}{p}$ stay constant along irreducible components of the zero set of $p$, and that the presence of vertical line singularities does not affect global integrability. This answers Question 2 in arXiv:1906.10913. Those results are then generalized to $n$ variables. Finally, we consider slice matrices, which we use to obtain derivative integrability conditions of unidirectional compositions $ϕ^N$. We present several new examples, including an RIF with two vertical line singularities and one with vertical surface singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26805",
  "author_total": 1,
  "authors": [
    {
      "name": "Leonora Krajina"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bz2g707b62whx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26805",
  "fulltext_url": null,
  "id": "bz2g707b62whx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26805",
  "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.CV"
    ],
    [
      "openalex",
      "2604|Holomorphic and Operator Theory"
    ]
  ],
  "openalex": "W7214207196",
  "pdf_url": "https://arxiv.org/pdf/2609.26805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bz2g707b62whx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.26805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Higher-dimensional singularities of rational inner functions",
  "title_text": "Higher-dimensional singularities of rational inner functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/bz2g707b62whx",
  "venue": "arXiv",
  "versions": []
}