{
  "abstract": "In this paper, we provide a systematic comparison between the equisingularity of a 1-parameter unfolding $F = (f_t, t)$ of a finitely determined map germ $f: (\\mathbb{C}^2, 0) \\to (\\mathbb{C}^3, 0)$ and the equisingularity of its associated families of double point curves: $D(F)$, $F(D(F))$, $D^2(F)$, and $D^2(F)/S_2$. We also construct explicit counterexamples to several natural questions concerning the equisingularity of these loci. As a key application, we introduce new families of complete intersection curves -- referred to as Henry--type families -- which are topologically trivial but fail to satisfy the Whitney equisingularity conditions. Finally, we generalize classical formulas for double point curves, originally established for map germs from $(\\mathbb{C}^2, 0)$ to $(\\mathbb{C}^3, 0)$, to the higher-dimensional setting of map germs from $(\\mathbb{C}^n, 0)$ to $(\\mathbb{C}^{2n-1}, 0)$ for $n \\geq 3$, thereby endowing the associated curves with a convenient analytic structure.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.08507",
  "author_total": 2,
  "authors": [
    {
      "name": "Otoniel Nogueira da Silva"
    },
    {
      "name": "Manoel Messias da Silva Júnior"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59n31t9w2zh79.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.08507",
  "fulltext_url": null,
  "id": "59n31t9w2zh79",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.08507",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7160961338",
  "pdf_url": "https://arxiv.org/pdf/2605.08507",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/59n31t9w2zh79.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2605.08507",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.08507"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Equisingularity in families of double point curves",
  "title_text": "Equisingularity in families of double point curves",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/59n31t9w2zh79",
  "venue": "arXiv",
  "versions": []
}