{
  "abstract": "We study robust features of smooth surfaces in 4-space associated with contact with lines and hyperplanes. We investigate the local and multi-local singularities of orthogonal projections and height functions that describe these contacts and their corresponding geometric loci on the surface. At an $A_4$-singularity of a height function, we show that the $A_3$-curve and the $A_1A_2$-curve are generically tangent with contact of order $2$. We further establish criteria for the versality of the families of height functions and orthogonal projections in terms of the regularity of the $B_2$-curve and $S_2$-curve, respectively. Finally, we obtain the $[A_2]$- and $(A_0S_0)_2$-curves arising from multi-local singularities of orthogonal projections and describe their tangency properties at the $B_3$- and $H_3$-singularities.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40604",
  "author_total": 1,
  "authors": [
    {
      "name": "Jorge Luiz Deolindo-Silva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53zrqbq2tvc7e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40604",
  "fulltext_url": null,
  "id": "53zrqbq2tvc7e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40604",
  "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.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40604",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53zrqbq2tvc7e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40604",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40604"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Some remarks on robust features of surfaces in 4-space",
  "title_text": "Some remarks on robust features of surfaces in 4-space",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/53zrqbq2tvc7e",
  "venue": "arXiv",
  "versions": []
}