{
  "abstract": "We study hyperelliptic curves on $K3$ surfaces. We show that any number of general points on a $K3$ surface of Picard rank one can be connected by a hyperelliptic curve. As a by-product we recover the Beauville--Voisin decomposition of the small diagonal, together with some new bounds on its torsion order in the integral Chow group. On the arithmetic side, given a $K3$ surface $X$ of geometric Picard rank one defined over a number field $k$, we show that there exists a finite extension $k\\subset k'$ such that quadratic points are dense in $X_{k'}$, extending a theorem of Corvaja--Zucconi to $K3$ surfaces of arbitrary degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17536",
  "author_total": 1,
  "authors": [
    {
      "name": "Federico Moretti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c9d6e31gqayjz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17536",
  "fulltext_url": null,
  "id": "c9d6e31gqayjz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17536",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221816058",
  "pdf_url": "https://arxiv.org/pdf/2610.17536",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c9d6e31gqayjz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17536",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17536"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Hyperelliptic curves on $K3$ surfaces",
  "title_text": "Hyperelliptic curves on K3 surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/c9d6e31gqayjz",
  "venue": "arXiv",
  "versions": []
}