{
  "abstract": "A $\\mathbb{Q}$-homology quadric is a smooth compact complex surface which has the same $\\mathbb{Q}$-homology as a quadric surface, that is, the product of two $2$-dimensional spheres. It is called fake if it is minimal and not rational. Among them are the fake quadrics which are isogenous to a product of complex curves. In this paper, we determine the parity of the intersection forms of all fake quadrics isogenous to a product of unmixed type. In particular, we show that there are fake quadrics with odd intersection forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06077",
  "author_total": 4,
  "authors": [
    {
      "name": "Fabrizio Catanese"
    },
    {
      "name": "JongHae Keum"
    },
    {
      "name": "Do Geun Kim"
    },
    {
      "name": "Kyoung-Seog Lee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cfcedc6g5d4t2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06077",
  "fulltext_url": null,
  "id": "cfcedc6g5d4t2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06077",
  "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"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cfcedc6g5d4t2.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CV",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Odd and even fake quadrics isogenous to a product",
  "title_text": "Odd and even fake quadrics isogenous to a product",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/cfcedc6g5d4t2",
  "venue": "arXiv",
  "versions": []
}