{
  "abstract": "We prove that the smooth affine hypersurfaces \\[ X_{m,n}=\\{ζ^mz_0^n+ (1+z_1ζ)z_2+ζz_3^2=1\\}\\subset\\mathbb{C}^5,\\;\\; m,n\\geq 2, \\] have the density property. For every odd integer $d\\geq 3$, we identify $X_{d-1,d}$ with a Kaliman modification along a Brieskorn variety of type $(d,2,2,2)$. We prove that the fourfolds $X_{d-1,d}$ are diffeomorphic to $\\mathbb{C}^4$ but not biholomorphic to $\\mathbb{C}^4$. These, therefore, give counterexamples to the Tóth-Varolin conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27660",
  "author_total": 1,
  "authors": [
    {
      "name": "Sushil Gorai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6pn89fnk0bna4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27660",
  "fulltext_url": null,
  "id": "6pn89fnk0bna4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27660",
  "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"
    ],
    [
      "arxiv",
      "math.CV"
    ],
    [
      "openalex",
      "2608|Geometry and complex manifolds"
    ]
  ],
  "openalex": "W7223102534",
  "pdf_url": "https://arxiv.org/pdf/2610.27660",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6pn89fnk0bna4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27660",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27660"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A new class of smooth algebraic varieties with the density property and a counterexample to the Tóth-Varolin Conjecture",
  "title_text": "A new class of smooth algebraic varieties with the density property and a counterexample to the Tóth-Varolin Conjecture",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6pn89fnk0bna4",
  "venue": "arXiv",
  "versions": []
}