{
  "abstract": "In 1929, O. Zariski found a pair of complex plane algebraic curves of the same degree and with the same collection of singularities, but embedded into the plane in a topologically different way. Accordingly, such curves belong to different components of the equisingular family. This phenomenon has been intensively studied till now. In this note, we propose a different insight on this subject: Two curves $C',C''\\subset\\PP^2$ form an {\\it anti-Zariski pair}, if $(\\PP^2,C')$ and $(\\PP^2,C'')$ are homeomorhic, but $C'$ and $C''$ belong to different components of the equisingular family. We exhibit examples of anti-Zariski pairs and discuss related issues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.20268",
  "author_total": 2,
  "authors": [
    {
      "name": "Peng Ren"
    },
    {
      "name": "Eugenii Shustin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fwc2c7swg6jzk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.20268",
  "fulltext_url": null,
  "id": "fwc2c7swg6jzk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.20268",
  "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": "W7165405918",
  "pdf_url": "https://arxiv.org/pdf/2606.20268",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fwc2c7swg6jzk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2606.20268",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.20268"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Anti-Zariski pairs",
  "title_text": "Anti-Zariski pairs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/fwc2c7swg6jzk",
  "venue": "arXiv",
  "versions": []
}