{
  "abstract": "Let $(C_{f},0) \\subset (\\mathbb{C}^{n},0)$ be a germ of an irreducible holomorphic curve, given implicity by $f(x)=0$ if $n=2$ and by $f(x)=g(x)=0$ if $n=3$, and parametrised by $γ:(\\mathbb{C},0) \\rightarrow (\\mathbb{C}^{n},0)$. We define the contact invariants $\\operatorname{Iso}_{f}$ and $\\operatorname{Iso}_γ$ for $f$ and $γ$, respectively, which count the number of isotropic points that appear after a generic deformation of the curve. We first consider the case where the curve is regular and establish a relation between those invariants and the number of vertices, inflection points and the zero-torsion points (for $n=3)$ that emerge from the deformation of the curve. Furthermore, we consider a germ of a singular curve with an isolated singularity and relate the number of isotropic points with the Milnor number of $f$",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06440",
  "author_total": 3,
  "authors": [
    {
      "name": "Amanda Dias Falqueto"
    },
    {
      "name": "Juan J. Nuño Ballesteros"
    },
    {
      "name": "Raúl Oset Sinha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55r8fngbqr5v3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06440",
  "fulltext_url": null,
  "id": "55r8fngbqr5v3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06440",
  "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/2611.06440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55r8fngbqr5v3.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On isotropic points and contact invariants of curves",
  "title_text": "On isotropic points and contact invariants of curves",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/55r8fngbqr5v3",
  "venue": "arXiv",
  "versions": []
}