{
  "abstract": "Let $X$ be a del Pezzo surface of degree $4$ over a field~$k$, and let $\\rho(X)$ denote its Picard rank. We prove that if the index of $X$, that is, the greatest common divisor of the degrees of its closed points, is equal to $2$, then $X$ has a closed point of degree $2$ or $6$. This result is optimal, as shown by examples due to Creutz and Viray. Moreover, if $\\rho(X)\\geq 2$, then $X$ has a closed point of degree $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Jean-Louis Colliot-Thélène"
    },
    {
      "name": "Federico Scavia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmt2bf7r92azy.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "fmt2bf7r92azy",
  "issns": [],
  "landing_url": "https://hal.science/hal-05852639v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ag"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05852639/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmt2bf7r92azy.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:44Z",
      "native_id": "hal-05852639",
      "source": "hal",
      "url": "https://hal.science/hal-05852639v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ag",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Closed points on del Pezzo surfaces of degree 4 and index 2",
  "title_text": "Closed points on del Pezzo surfaces of degree 4 and index 2",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:44Z",
  "url": "https://research.draconitic.com/paper/fmt2bf7r92azy",
  "venue": "HAL",
  "versions": []
}